Electrostatics
Electrostatics is the study of electric charges that are not moving. This unit explains the two kinds of charge, how objects become charged by friction, contact and induction, and how conductors and insulators differ at the atomic level. It then introduces the electric field and its field lines, and applies these ideas to the electroscope, the electrostatic precipitator, the photocopier, electrical breakdown and lightning, including how a lightning rod protects a building.
Learning outcomes (19)
- State that there are positive and negative charges.
- State that unlike charges attract and like charges repel.
- Describe experiments to show electrostatic charging by friction.
- Explain that charging of solids by friction involves only a transfer of negative charge (electrons).
- Explain how and why an insulator can be discharged by (a) putting it above a flame, and (b) exposing it to damp conditions.
- Explain how a conductor can be charged by electric induction and then "earthing".
- Describe examples where charging could be a problem, for example lightning.
- Suggest how charging and discharging is used in the application of various devices.
- Describe an electric field as a region in which an electric charge experiences a force.
- State that the direction of an electric field line at a point is the direction of the force on a positive charge at that point.
- Analyse and illustrate simple electric field patterns.
- State examples of electrical conductors and insulators.
- Describe an experiment to distinguish between electrical conductors and insulators.
- State and use a simple electron model to explain the difference between electrical conductors and insulators.
- Explain how a lightning rod can protect humans.
- Explain electrical breakdown.
- State that corona discharge and Lichtenberg figures are visible examples of electrical breakdown.
- Explain how lightning is generated.
- State that there are many kinds of atmospheric lightning.
15.1Static charge
Electrostatics is the study of electric charges that are not moving, which is where the name comes from. Have you ever felt your hair stand up after brushing it, or felt a small jolt on touching a doorknob after leaving a car? These everyday effects are caused by the electrostatic force, the hidden power of electric charge (Figure 15.1).
Electric charge is measured in coulombs (symbol C). The unit is named after the French physicist Charles A. de Coulomb (1736–1806), who discovered a relationship between electric force and charge.
Charge inside the atom
Everything around you, from your hair and clothes to the doorknob, is built from tiny building blocks called atoms. Inside an atom there are even smaller particles. Some carry a positive charge (+) and are called protons; they sit in the nucleus. Others carry a negative charge (−) and are called electrons; they form a cloud around the nucleus. Neutrons have no charge and are also found in the nucleus. Figure 15.2 shows the simplest atom, hydrogen, and Table 15.1 lists the charges and masses of the three particles.
| Particle | Charge (C) | Mass (kg) |
|---|---|---|
| electron | ||
| proton | ||
| neutron |
There are two kinds of charge
How do you know that charges are of two types? Rub a glass rod vigorously with a silk cloth and hang it up. Bring a second glass rod, rubbed with silk in the same way, close to it. The two glass rods push each other away. The same happens with two ebonite (hard rubber) rods rubbed with fur.
Now hang a glass rod rubbed with silk and bring an ebonite rod rubbed with fur near it. This time the rods are pulled towards each other. The same happens if the ebonite rod is hung and the glass rod is brought near.
This experiment shows that there are two types of charge: like charges repel, while opposite (unlike) charges attract. By Newton's third law of motion, the force of repulsion or attraction on one rod is equal in size and opposite in direction to the force on the other rod, and the two forces act on different objects.
15.1.1Charge is conservedOften examined
Charge cannot be created or destroyed. So how does an object become charged? When objects are charged, electric charge is not actually created; it is simply transferred from one object to another. This transfer of charge is called electrification.
The excess charge is almost always produced by a transfer of electrons, not protons. Protons are bound in the nucleus and, in common situations, stay fixed (their mass in Table 15.1 is also far greater than that of an electron). Electrons in the outer part of the atom are the ones that can move from one body to another.
Charging a glass rod and a rubber rod
When a glass rod is rubbed with a silk cloth, both the rod and the cloth become charged. Electrons move from the glass rod to the silk cloth. The glass rod, which has lost electrons, is positively charged. The silk cloth, which has gained electrons, is negatively charged. This silk cloth will repel a hanging rubber rod that has been rubbed with fur, in the same way as another rubber rod rubbed with fur does.
Similarly, when a rubber rod is rubbed with animal fur, electrons move from the fur to the rubber rod. The rubber rod becomes negative and the fur becomes positive.
| Rubbed pair | Loses electrons | Gains electrons | Charge on the rod |
|---|---|---|---|
| glass rod and silk cloth | glass rod | silk cloth | positive |
| rubber (ebonite) rod and animal fur | animal fur | rubber rod | negative |
When you charge an object, you either add or remove electrons. If you remove electrons the object has a positive charge; if you add electrons it has a negative charge. The number of protons in the object stays the same in both cases. The net charge on a solid is therefore due to an excess or a deficiency of electrons.
- electrons transferred
- charge of one electron
- charge on rod and on cloth
- total charge
- number of electrons for
- Charge is made of whole electrons, so the charge moved is the number of electrons times the charge of one electron.
- The rod lost electrons, so it is positive. The cloth gained the same electrons, so it carries the same amount of negative charge.
- Add the two charges. The total is unchanged from the zero before rubbing: charge was transferred, not created.
- For part (c) divide the charge wanted by the charge of one electron to count the electrons removed.
15.2Conductors and insulatorsOften examined
Materials are divided into conductors and insulators by their ability to conduct, or carry, electric charge. Metals are efficient conductors of electric charge. Glass, rubber and most plastics are insulators, or poor conductors.
In a conductor the valence electrons, which are the electrons in the outermost atomic orbits, are loosely bound to their atoms. This loose binding lets them be detached easily, so they move freely inside the conductor and can even leave it altogether (Figure 15.4(a)). These mobile electrons are called free electrons. Because of them a conductor transfers electric charge efficiently.
In an insulator even the least tightly bound electrons are firmly attached to their atoms. They cannot move freely, so charge cannot flow through the material. Electric charge cannot easily be redistributed or removed from an insulator, which makes it ineffective at conducting charge (Figure 15.4(b)).
| Conductor | Insulator | |
|---|---|---|
| Outer electrons | loosely bound, free to move | firmly bound to their atoms |
| Charge movement | flows easily through the material | cannot flow through the material |
| Examples | metals such as copper and aluminium | glass, rubber, plastic, wood |
How charge sits on a conductor and on an insulator
When a charge is placed on a spherical conductor it spreads out evenly over its surface. On other shapes, the charges repel one another and move towards the more pointed parts (Figure 15.5(a)). An insulator does not let charges move easily, so the charge stays in the spot where it was put (Figure 15.5(b)).
So if you charge one part of an insulator, for example by rubbing wool on a plastic rod, the charge stays in that area while the rest of the rod remains neutral.
Telling a conductor from an insulator by experiment
Charge a gold-leaf electroscope (section 15.4) so that its leaf stands out. Connect the electroscope cap to the earth through the material under test, for example by touching the cap with one end of the material while the other end is held in the hand or joined to the ground. If the material is a conductor, the charge flows away through it and the leaf collapses. If it is an insulator, the charge cannot escape and the leaf stays raised. The same idea works when a metal rod and a plastic rod are touched in turn to a charged object.
15.3Charging and dischargingOften examined
Sliding across a car seat moves electrons between materials and leaves an accumulation of negative charge on your body. This electrostatic charge stays where it is (it is "static") and is produced by friction between the surfaces. It remains until the electrons can spread out because they repel one another. When you reach for a metal doorknob the electrons find an escape route and you see a spark. A metal doorknob is a good conductor, so electrons can move freely through it. If you touch plastic or wood you feel no shock.
There are three main ways to charge objects: through friction, contact and induction.
| Method | What happens | Charge gained |
|---|---|---|
| Friction (rubbing) | two different materials are rubbed together and electrons pass from one to the other | the two objects get opposite charges |
| Contact (conduction) | a charged object touches a neutral object and some charge passes across | the neutral object gets the same kind of charge as the charged object |
| Induction | a charged object is brought near, without touching, and the charges in the neutral object separate | with earthing, a net charge opposite to that of the charged object remains |
15.3.1Charging by friction
Friction is a basic way for charge to be transferred between objects. The direction and the amount of the transfer depend on two properties of atoms: ionization energy and electron affinity.
The nucleus of an atom attracts the mobile electrons in its outer orbitals. The stronger the attraction, the more energy is needed to remove an electron. Removing an electron from an atom ionizes the atom.
- Ionization energy
- The energy needed to remove the outermost electron from an atom.
Electron affinity describes how strongly an atom attracts an extra electron. When two different materials are rubbed together, electrons pass from the material whose atoms hold them less strongly to the material whose atoms attract them more strongly. This is why the glass rod loses electrons to silk and the fur loses electrons to the rubber rod (section 15.1.1).
15.3.2Charging by contact (conduction)
When a charged object touches a neutral object, the excess or deficit of electrons on the charged object makes charge pass to the neutral object. In Figure 15.6, a negatively charged object gives some of its excess electrons to the neutral object, which therefore becomes negatively charged. A positively charged rod, on the other hand, pulls electrons out of a neutral object and leaves it with an overall positive charge.
15.3.3Charging by inductionOften examined
Imagine a negatively charged rubber strip held near an insulated metal sphere X that touches a second sphere Y (Figure 15.7(a)). The negative charge on the strip repels the electrons in sphere X and pushes them towards the far side of the connected sphere Y. This creates a temporary separation of charge: an excess of negative charge on the far side of Y and a shortage of electrons on the near side of X. Importantly, no electrons pass from the strip to the spheres.
Now separate sphere X from sphere Y while the charged strip is still nearby (Figure 15.7(b)). The separated charges are "frozen" in place. Sphere X, which lost electrons, becomes positively charged. Sphere Y, which holds the repelled electrons, becomes negatively charged. When the strip is taken away, the charge spreads over each sphere (Figure 15.7(c)). This is a way of using electrostatic induction to separate charges and create charged objects.
From these two activities it follows that bodies can be charged by a process called electrostatic induction.
- Electrostatic induction
- A change in the distribution of electrical charge in an object, caused by the influence of nearby charges.
Induction with earthing (grounding)
One way to charge a conductor by induction is by grounding it. This means connecting a neutral object to the ground for a short time so that extra charges can escape. Suppose a negatively charged object is brought close to a neutral metal sphere. The positive charges in the sphere are drawn towards the charged object and the negative charges are pushed to the side away from it, so the electrons move away from the side that faces the charged object. Earthing (grounding) means giving charge a path along which it can escape into the ground. If the sphere is touched briefly with a finger, the extra electrons flow through the finger into the ground, and the sphere is left with a net positive charge (Figure 15.8).
- Bring the charged rod near the neutral conductor without touching it. The conductor's charges separate: electrons move away from the rod.
- Touch the conductor (or connect it by a wire) to the earth while the rod is still near. The electrons that were pushed away escape into the ground.
- Remove the earth connection while the rod is still near. The conductor now has fewer electrons than protons.
- Take the rod away. The remaining charge spreads over the conductor, which now has a net charge opposite to that of the rod.
- Hold the positive rod near the sphere without touching it. The rod attracts the sphere's free electrons towards the near side, so the near side becomes negative and the far side is left with a shortage of electrons, so it is positive.
- Touch the sphere with a finger or connect it to the earth. Electrons flow from the earth into the sphere and cancel the positive charge on the far side.
- Remove the earth connection first while the rod is still near. The extra electrons are now trapped on the sphere.
- Remove the rod. The extra electrons, which repel one another, spread evenly over the surface of the sphere.
The sphere ends up with the opposite charge to the rod, and the rod itself loses no charge. This is different from charging by contact, where the sphere would take the same kind of charge as the rod.
15.3.4Methods to discharge insulators
Electrical discharging is the process of neutralizing or dissipating electric charge on a material or surface. In conductors this happens when the excess charge is redistributed or flows away through a conducting path, returning the material to a neutral state. Conductors can be discharged by grounding them or by applying an opposite charge. Insulators resist the flow of charge, but they too can be discharged under certain conditions.
Discharging an insulator usually requires changing the environment of the material so that charge can move or be neutralized. Two effective techniques are heating it over a flame and exposing it to damp (humid) conditions.
A. Heating above a flame. When an insulator is heated with a flame, the heat excites the electrons and can make the surrounding air conductive, which helps to neutralize the charge. The heat can also temporarily increase the surface conductivity of the insulator, so the static charges can move and discharge (Figure 15.9(a)).
B. Exposing to humid conditions. Placing an insulator in damp air promotes discharge because water molecules stick to its surface. These polar molecules interact with the charged areas and form a thin conductive layer that lets charge move. In addition, the ions present in humid air help to neutralize the static charge on the surface of the insulator, which makes this an effective discharging method (Figure 15.9(b)).
15.3.5A surface charge can be induced on insulators by polarization
Run a plastic comb or brush through your hair. Some electrons move from your hair to the comb, which becomes negatively charged. Now hold the comb near small pieces of paper. The pieces, which have a balanced charge, jump towards the comb. How is this possible? Why does a neutral object get attracted rather than repelled?
The paper starts with equal numbers of positive and negative charges. The negatively charged comb creates an electric field around it as it approaches the paper. The negative charge on the comb repels the negative charges in the paper but attracts the positive charges. The positive charges therefore move closer to the comb while the negative charges are pushed away. In the end, the attraction between the comb and the positively charged near side of the paper is stronger than the repulsion between the comb and the negative charges farther away. This net attraction pulls the paper towards the comb, like a tug-of-war won by the nearer, attracting side.
The same effect is seen with a plastic (or amber) rod rubbed with fur (Figure 15.10(a) and (b)). A balloon rubbed against hair can also attract a falling stream of water (Figure 15.10(c) and (d)).
- Induced polarization
- When a charged object is brought near an insulator, the electric field of the charged object redistributes the charges within the insulator, creating a slight separation of positive and negative charges.
- The positive rod attracts the free electrons of the ball to the near side and leaves the far side short of electrons. The near side becomes negative and the far side positive.
- The unlike charges on the near side are closer to the rod than the like charges on the far side. The attraction is therefore stronger than the repulsion, and the ball swings towards the rod.
- On touching, some electrons pass from the ball to the positive rod. The ball is now short of electrons and has a net positive charge (charging by contact).
- The ball and the rod now have the same kind of charge, so they repel and the ball is thrown away.
15.4ElectroscopeOften examined
The electroscope is an essential device for detecting and analysing the charge present on an object. It works on the principle that like charges repel and unlike charges attract.
A basic electroscope consists of a metal bar with a metal disk at its upper end. A thin, flexible gold leaf (or another metal such as silver or copper) is attached to the lower end of the bar. The lower part of the electroscope is enclosed in an insulated housing (Figure 15.11).
Detecting a charge
To use the electroscope, touch the metal disk with the object to be tested. For example, if you touch the disk with a negatively charged plastic rod, some of the rod's excess electrons pass to the disk. They spread through the metal bar and the gold leaf by electrostatic induction. The leaf and the bar now carry the same kind of charge, so the flexible leaf repels the bar and rises higher. In the same way, if a positively charged rod is brought near the metal disk, it attracts electrons from the electroscope and leaves the disk with a net positive charge. Again the leaf rises.
When a charged rod is brought near an uncharged electroscope, it shows that the rod is charged, but it does not tell us the sign of the charge.
Finding the sign of a charge
The sign can be found if the electroscope is first given a known kind of charge. For instance, give the electroscope a negative charge by transferring electrons to it from a negatively charged object. The electrons repel one another, and some pass to the leaf, which diverges from the bar (Figure 15.12(a)). If a negatively charged rod is now brought close to the electroscope, more electrons are repelled down to the leaf and it diverges even further (Figure 15.12(b)). A positively charged rod, on the other hand, attracts electrons up to the disk and away from the leaf, so the leaf collapses (Figure 15.12(c)).
| Electroscope charged | Rod brought near the disk | Leaf | Sign of the rod |
|---|---|---|---|
| negative | negative | rises further | negative |
| negative | positive | falls (collapses) | positive |
| positive | positive | rises further | positive |
| positive | negative | falls (collapses) | negative |
Charging an electroscope by induction
It is possible to give an electroscope a positive charge using a negatively charged rubber rod, by induction. The electroscope is earthed with a finger so that electrons can escape from the disk to the ground (Figure 15.13). When the negatively charged rod is brought close to the disk, electrons are repelled through the finger and the body to the Earth. If the finger is removed while the charged rod is kept nearby, the electroscope is left with a net positive charge.
- Case (a): the positive rod repels positive charge. Electrons in the electroscope are attracted up to the disk. The leaf and bar lose electrons and become more positive, so they repel each other more and the leaf rises further.
- Case (b): the negative rod repels electrons down the bar to the leaf. These cancel some of the positive charge there, so the leaf and bar are less positive, they repel less and the leaf falls.
- For an unknown rod, a leaf that falls when the rod is brought near a positively charged electroscope shows that the rod is negatively charged. A leaf that rises further shows that the rod is positive.
15.5Electric fieldOften examined
One charge exerts a force on another charge. This force is present everywhere around the charge and in theory it extends to infinity, but its strength decreases with distance. The region around a charge where it can attract or repel another charge is described by the concept of the electric field.
- Electric field
- The region around a charge where it exerts a force on other charges.
The electric field strength decreases with distance from the charge, following an inverse square law for point charges. So although the field is theoretically present everywhere, its influence becomes smaller as the distance grows.
For the electric force to act on a charged particle, the charges do not have to touch. The force is there whenever a test charge is brought into the electric field of a charge (usually called the source charge). Consider a test charge placed in the electric field of a source charge (Figure 15.14). The source charge exerts an electrostatic force on the test charge.
- Electric field intensity
- The electrostatic force per test charge (per unit positive charge) when it is brought into the electric field of a source charge.
The SI unit of electric field intensity is (newton per coulomb). Electric field intensity (electric field strength) is a vector quantity: it has both magnitude and direction. The direction of the electric field intensity at a point is the direction of the force on a positive test charge placed at that point.
Rearranging Equation 15.2 gives the force on a charge placed in a field of strength .
A positive charge feels a force in the direction of . A negative charge feels a force of the same size in the opposite direction.
- test charge
- electric field strength
- The electric field intensity is the force per unit test charge.
- Put in the values.
- Evaluate.
The field strength at this point is .
- to the right
- at P
- on the second charge
- (a) Use the definition of field strength with the first charge.
- The force on a positive charge is to the right, so the field at P also points to the right.
- (b) The field at P is a property of the point, not of the charge placed there. Use with the new charge.
- The charge is negative, so the force is opposite to the field: to the left.
- (c) At P, with the same for every charge, so is proportional to . The graph is a straight line through the origin. Check the gradient: , the field strength.
How the field changes with distance
For a point charge the field strength follows an inverse square law, so it falls quickly with distance. If is the strength at distance , then at it is and at it is .
15.5.1Electric field linesOften examined
To picture the electric field around a source charge, the direction of the force on a positive test charge is drawn as a line. This line gives the direction of the electric field intensity at that point or region, and so these lines are called electric field lines. They were first introduced by Michael Faraday. Field lines are imaginary and have no physical existence.
For a positive charge, the field lines are directed away from the charge, because a positive charge repels a positive test charge (Figure 15.15(a)). For a negative charge, the field lines are directed towards the charge, because it attracts a positive test charge brought into its field (Figure 15.15(b)).
Figure 15.16(a) shows the symmetric field lines of a pair of point charges of equal size and opposite sign. Such a pair forms an electric dipole. The lines start on the positive charge and end on the negative charge. The crowded lines between the charges show a powerful electric field in that region, particularly between the two charges.
Figure 15.16(b) shows two particles with the same kind of charge (both positive). They repel each other. The field lines show the direction and strength of the field around the charges: the lines from the two charges bend away from each other and do not join.
Field of a charged conducting sphere
The electric fields of charged conductors have interesting properties. A charged conducting sphere makes an electric field that spreads out uniformly if the sphere is positive (Figure 15.17), or points inwards if it is negative. Outside the sphere the field behaves like that of a point charge, decreasing with distance according to the inverse square law. Inside the sphere the electric field is zero, because the charges distribute themselves evenly on the surface and produce a balanced field within. A point charge, in contrast, produces a field that spreads out from a single point and decreases with the inverse square of the distance, without any interior region.
Field between two parallel plates
Another important example is two parallel plates that are oppositely charged: one plate is positive and the other negative (Figure 15.18). The two plates get their charge by being joined to a battery. The electric field in the region between them is uniform, which means that both the strength and the direction of the field stay constant throughout the space between the plates. The field lines run in straight parallel paths from the positive plate to the negative plate and show the direction in which a positive charge would move. This uniformity is an important property of the field between parallel plates, because it simplifies calculations and predictions about charged particles in the field.
- E = 2.5\times10^{3}\,\mathrm{N\,C^{-1}}
- q = -1.6\times10^{-19}\,\mathrm{C} electron
- magnitude and direction of F
- (a) The field lines run from the positive plate to the negative plate, so E points to the right. The force on a positive charge would be to the right, but the electron is negative, so the force on it is to the left, towards the positive plate.
- (b) Use F=qE and take the magnitude of the charge.F=|q|E=1.6\times10^{-19}\times2.5\times10^{3}
- Multiply the numbers and add the powers of ten.F=4.0\times10^{-16}\,\mathrm{N}
- (c) The field between the plates is uniform: its strength is the same at every point. So the force does not change when the electron moves.
15.6.1Electrostatic precipitator and dust extraction
Electrostatics has a number of applications in daily life. The first is the electrostatic precipitator, also called a dust extractor, which works on the principle of electrostatics. To reduce air pollution, coal-burning power stations use electrostatic precipitation to remove dust from the smoke in their chimneys before it is released into the environment (Figure 15.19).
Air mixed with dust enters the device across a positively charged mesh. The airborne particles become positively charged when they touch the mesh. They then pass through a second, negatively charged mesh. The electrostatic force of attraction between the positively charged particles in the air and the negatively charged mesh makes the particles precipitate out on the surface of the mesh.
15.6.2Photocopier machine
Most photocopying machines use an electrostatic process called xerography, from the Greek words "xeros" (dry) and "graphos" (writing). The main steps are: charging the photoconducting drum, transferring an image, creating a positive charge duplicate, attracting toner to the charged parts of the drum, and transferring the toner to the paper (Figure 15.20).
The process begins with a drum of aluminium coated with selenium, which is sprayed with a positive charge by a device called a corotron. Selenium is a photoconductor: it behaves as an insulator in the dark and becomes a conductor when it is exposed to light. This property lets the drum hold a static charge in the dark areas while it discharges in the areas that are exposed to light, so a hidden (latent) image is created on the surface of the drum. The toner particles, which are oppositely charged, are then attracted to the charged areas of the drum. Finally the toner is transferred to a piece of paper and fused on with heat and pressure, which gives a clear copy of the original document.
15.7Electrical breakdown
Insulating materials such as rubber, glass and some plastics do not normally conduct electricity. When the electric field is strong enough, however, they can reach a breakdown voltage. Electrons are then pulled out of their atoms and current can flow.
Gases are generally poor conductors too, but a strong electric field can ionize gas atoms, removing electrons and creating free electrons and positively charged ions. The gas can then conduct electricity. This can set off an avalanche effect, in which freed electrons collide with other atoms and cause further ionization.
Visible examples
Corona discharge and Lichtenberg figures show how electrical breakdown happens.
Corona discharge appears as a faint glow around sharp points or edges of conductors at high voltage. It occurs because the air molecules around the conductor become ionized, which causes a localized breakdown. You can see this effect around power lines (Figure 15.21) or during thunderstorms.
Lichtenberg figures are intricate branching patterns formed on insulating surfaces such as acrylic or glass (Figure 15.22) when they are subjected to a high-voltage discharge. They are a visual record of the path taken by the electric current as it travels through the material, leaving behind permanent tree-like patterns. Both phenomena clearly demonstrate electrical breakdown in different situations.
15.7.2Lightning generation
Lightning is a powerful release of electrical energy that occurs in clouds when air, water droplets or volcanic ash collide and cause electrical charges to separate. Positive charges rise to the top of the cloud, while negative charges sink. As the cloud becomes more highly charged, a conducting plasma forms. Excess electrons at the base of the cloud travel towards the ground in a zigzag pattern called a step leader.
The negative charge at the bottom of the cloud induces a positive charge on the surface of the Earth, which is a polarized effect. Nearby air molecules ionize and rise, forming a positive charge known as a streamer. When the streamer meets the step leader, a complete path is established and a lightning strike results, with negative charge moving to the ground at speeds of up to 100\,000\,\mathrm{km\,s^{-1}}.
- Air, water droplets or volcanic ash collide inside the cloud, and electrical charges separate.
- Positive charges rise to the top of the cloud and negative charges sink to its base.
- The strong field forms a conducting plasma, and excess electrons from the base travel downwards in a zigzag step leader.
- The negative base induces positive charge on the ground. Ionized air rises as a positive streamer.
- The streamer meets the step leader, a complete conducting path forms and the lightning strike discharges the cloud.
15.7.3Varieties of atmospheric lightning
Lightning is not limited to the common cloud-to-ground strike. Most lightning occurs entirely within a cloud (intracloud discharges), where it cannot be seen. Visible discharges do take place between clouds (cloud-to-cloud discharges) and between a cloud and the Earth (cloud-to-ground discharges). There are also many fascinating, less understood types of lightning that occur high in the atmosphere, such as:
- Sprites: short-lived, red flashes above thunderstorms.
- Jets: narrow, upward bursts of blue light.
- Elves: expanding rings of faint, white light.
- Others with even more whimsical names, such as trolls, pixies, ghosts and ball lightning. These are all being actively researched by scientists.
| Kind of lightning | Where it occurs |
|---|---|
| intracloud | within a single cloud (usually hidden from view) |
| cloud-to-cloud | between two clouds |
| cloud-to-ground | between a cloud and the Earth |
| sprites, jets, elves and others | high in the atmosphere above thunderstorms |
15.7.4Uncontrolled charging and lightning rodsOften examined
Uncontrolled electrical charging in nature can lead to serious problems, such as lightning. When clouds accumulate positive and negative electricity, the air can no longer insulate, and a lightning strike can damage property, harm people and start fires.
To stay safe during thunderstorms, take shelter in a sturdy building. If you are outside, crouch with your feet together and stay away from tall objects and water.
Lightning is destructive because it sends very strong currents through poor conductors, which creates extreme heat that can endanger buildings. A lightning rod, invented by Benjamin Franklin in the 1750s, helps to protect structures. It is a pointed metal rod placed on top of a building and connected to a buried rod (Figure 15.23). This system attracts the lightning and gives its current a safe path to the ground, which prevents damage and stops harmful electrical surges.
- In a thunderstorm, negative charges collect in the lowest part of the cloud. Their electric field repels electrons on the ground and induces a positive charge there.
- The strong field accelerates electrons and ions and causes a chain reaction in the air that forms plasma. The ionized air is a conductor and it branches out from the cloud as step leaders.
- Positive charges spark out from the lightning rod and meet the step leader. The conducting path is now complete and the current neutralizes the separation of charge. Even if the strike does not hit the rod directly, the huge current can still leap to the rod, which is the path of least resistance to the ground.
- The current travels safely through the conductor to the ground terminal.
Formula sheet
Key terms
- Electrostatics
- The study of electric charges that are not moving.
- Coulomb
- The SI unit of electric charge, symbol C, named after the French physicist Charles A. de Coulomb.
- Proton, electron and neutron
- Proton: positive particle in the nucleus (+1.6\times10^{-19}\,\mathrm{C}). Electron: negative particle outside the nucleus (-1.6\times10^{-19}\,\mathrm{C}). Neutron: uncharged particle in the nucleus.
- Like and unlike charges
- Like charges repel one another; unlike (opposite) charges attract one another.
- Electrification
- The process by which an object acquires an electric charge, by friction, contact or induction.
- Conservation of charge
- The total electric charge in an isolated system remains constant: charge cannot be created or destroyed, only transferred between objects.
- Quantization of charge
- Electric charge exists in discrete units, those of the electron (negative) and the proton (positive), and cannot be divided further.
- Conductor
- A material that allows electric charge to flow freely through it because it has loosely bound (free) electrons, for example copper and aluminium.
- Insulator
- A material that resists the flow of electric charge because its electrons are tightly bound, for example rubber, plastic and wood.
- Free electrons
- The loosely bound outer (valence) electrons of a conductor, which are free to move through the material.
- Charging by friction
- Rubbing two dissimilar materials together so that electrons pass from one to the other.
- Ionization energy
- The energy needed to remove the outermost electron from an atom.
- Charging by contact
- A charged object touches a neutral object and electrons pass between them, so the neutral object gets the same kind of charge, to a lesser degree.
- Electrostatic induction
- A change in the distribution of electrical charge in an object caused by the influence of nearby charges, without touching.
- Earthing (grounding)
- Giving charge a path along which it can escape into the ground.
- Discharging
- The process by which an object loses its electric charge, by conduction, convection or a spark.
- Induced polarization
- The slight separation of positive and negative charge inside an insulator caused by the electric field of a charged object brought near it.
- Electroscope
- A simple instrument that detects the presence and the sign of electric charge; its leaf diverges when it is charged.
- Electric field
- The region around a charge where it exerts a force on other charges.
- Electric field intensity
- The electrostatic force per unit positive test charge in the field of a source charge: E=F_E/q_0, in \mathrm{N\,C^{-1}}.
- Electric field lines
- Imaginary lines whose direction at a point is the direction of the force on a positive charge there. They point away from positive charges and towards negative charges, and are closer together where the field is stronger.
- Electric dipole
- A pair of point charges of equal size and opposite sign.
- Uniform electric field
- A field with the same strength and direction everywhere, such as that between two oppositely charged parallel plates.
- Electrostatic precipitator
- A device that uses an electric field to remove dust and other pollutants from air by attracting the charged particles to collecting plates.
- Xerography
- The electrostatic process used by photocopiers: a charged photoconducting drum, an image, toner attracted to the charged parts, and toner transferred to the paper.
- Electrical breakdown
- The failure of an insulator, including a gas such as air, when a strong electric field pulls electrons from its atoms and lets current flow.
- Corona discharge
- A faint glow, or ionization of the air, caused by a strong electric field around a sharp point or edge of a conductor.
- Lichtenberg figures
- Branching, tree-like patterns left on the surface of an insulator when a high-voltage discharge passes through it.
- Lightning
- The rapid discharge of electricity within a cloud or between a cloud and the ground, caused by the build-up of charge in the cloud.
- Step leader and streamer
- The step leader is the zigzag path of electrons that travels from the cloud base towards the ground; the streamer is the positive charge that rises from the ground to meet it.
- Van de Graaff generator
- An electrostatic generator that uses a moving insulating belt to collect charge on a hollow metal globe at the top of an insulated column, giving very high voltages at low current.
- Lightning rod
- A pointed metal rod on a building, joined to a buried rod, which gives lightning current a safe path to the ground.
Multiple choice questionsp. 180–181
- ApositiveAnswer
- Bnegative
- Cneutral
- Dzero
Rubbing transfers electrons from the fur to the rubber rod, so the fur loses electrons and becomes positive. The positively charged fur is brought near the bulb, and the electrons in the uncharged electroscope are attracted up towards the bulb.
The electrons move up from the leaves, so the leaves are left short of electrons and carry a net positive charge. They repel each other and diverge. The rod is negative, but it is the fur that is brought near, so the fur decides the sign.
- ApositiveAnswer
- Bnegative
- Cneutral
- Dzero
The negative object repels electrons in the conductor, so they move to the far side. Grounding that side lets these electrons escape to the earth.
With the electrons gone, the conductor is left with a net positive charge while the object is still nearby. It is not neutral (C) or zero (D), because it has lost electrons; it is not negative (B), because it has lost, not gained, electrons.
- Apositive
- Bnegative
- Cpositive or neutral
- Dnegative or neutralAnswer
Unlike charges attract and like charges repel. A negative ball is attracted to a positive rod. A neutral ball is also attracted: the rod pulls its electrons towards the near side, which leaves that side slightly negative, and the induced charge attracts the ball.
A positive ball would be repelled, so options A and C are wrong. Option D is the only one that contains no positive ball.
- Aa neutral atom loses electronAnswer
- Ba neutral atom gains electron
- Cnegatively charged atom loses electron
- Dcan be true for all these cases
A positive ion has more protons than electrons. A neutral atom that loses an electron keeps all its protons but has one electron fewer, so it becomes positive: \mathrm{X}\rightarrow\mathrm{X}^{+}+e^{-}.
Gaining an electron (B) makes a negative ion. A negatively charged atom that loses an electron (C) becomes neutral, not positive. Option D is wrong because A is the only correct case.
- Auncharged
- Bcharged with different sign
- Ccharged with same signAnswer
- Dcan be true for all these cases
Repulsion happens only between like charges, so the suspended object must have a net charge of the same sign as the rod.
An uncharged object would be attracted, not repelled, because of induction (A). An object with the opposite sign would be attracted (B). So D is wrong.
- Aattract each other
- Brepel each otherAnswer
- Cexert no force on each other
- Dneutralize each other
When the spheres touch, electrons move from the negative sphere onto the neutral one until both are at the same potential. Charge is shared, not destroyed, so both spheres end up negatively charged.
Two like charges repel, so the spheres push apart (B). They do not attract (A) and they are not left without force (C). They cannot neutralize (D), because the total charge is conserved.
- Amagnitude
- BdirectionAnswer
- Cboth magnitude and direction
- Dneither magnitude nor direction
The force on the negative charge always points along the straight line joining the two charges, towards the positive charge. So the direction stays the same.
As the negative charge gets closer, the force grows, so the magnitude changes (A and C are wrong). The direction does not change, so D is wrong.
- Ain the middle of a grassy meadow.
- Binside a metal car.Answer
- Cnext to a tall tree in a forest.
- Don a metal observation tower.
A closed metal car is a conductor. Lightning charge spreads over its outside and passes to the ground through the metal body, so the people inside are shielded from the discharge.
A grassy meadow (A), a tall tree (C) and a tall metal tower (D) are the exposed or tall objects that attract lightning. The book advises avoiding tall objects.
- Aattraction of unlike charges
- Brepulsion of like chargesAnswer
- Cneutral nature of leaves
- Dair pressure
When the electroscope is charged, both leaves get charge of the same sign. Like charges repel, so the leaves move apart.
Attraction of unlike charges (A) would bring the leaves together. Neutral leaves (C) would not move, and air pressure (D) plays no role.
- Aflat surfaces
- Bsharp pointsAnswer
- Csmooth spheres
- Dinsulated areas
Charge on a conductor collects most where the surface is most curved. At a sharp point the charge is concentrated in a tiny area, so the electric field there is strongest. This strong field ionizes the air around the point and causes the faint glow of corona discharge.
Flat surfaces (A) and smooth spheres (C) have a weaker and more spread-out field. Insulated areas (D) do not carry charge, so no discharge forms there.
- Astraight lines
- Bcircular rings
- Cbranching tree-like patternsAnswer
- Drectangular shapes
Lichtenberg figures are branching, tree-like patterns left on an insulator's surface when a high-voltage discharge passes through it (Section 15.7.1).
Straight lines (A), circular rings (B) and rectangles (D) are not the patterns made by electrical breakdown.
Constructed response questionsp. 181–182
Draw two parallel, equal straight lines. Mark the left plate with + signs (positive) and the right plate with − signs (negative).
Between the plates the field is uniform, so the field lines are straight, parallel and equally spaced. They point from the positive plate to the negative plate, the direction in which a positive test charge would move.
Sketch of the field
Each charge is negative, so the field lines point towards each charge. Outside the ring the lines are drawn pointing radially inwards. Far from the ring the eight charges look like one large negative charge at the centre, so the lines converge on the ring.
Inside the ring the contributions of the eight charges cancel by symmetry. At the centre the field is zero, and no field lines pass through the inside of the ring.
Model of the field inside a coaxial cable
A coaxial cable has a central conductor surrounded by a hollow metal outer conductor (the shield). Charge on the outer conductor spreads evenly around a circle, which is what the eight equal charges represent.
The region enclosed by the outer conductor has zero field from the charge on that conductor, exactly as the inside of the ring has zero field. So the ring shows why the field inside the shielded part of the cable is zero. The ring model does not include the central conductor itself, which carries its own charge and produces the field between the two conductors.
The field lines point away from positive charges and towards negative charges. In the figure the lines leave the right-hand particle and end on the left-hand particle.
So the right-hand particle is positive and the left-hand particle is negative.
The strength of the field is shown by how close together the field lines are. Where the lines are farthest apart, the field is weakest.
Region D lies outside the outermost loop, far from both particles, where the lines are most widely spaced. So the field is weakest at D.
The field is strongest where the lines are closest together and nearest to the charges.
Region A lies between the two particles, close to the positive particle, where the lines are most crowded. So the field is strongest at A.
Short response questionsp. 182
Charging a metal by friction, contact or induction moves only electrons, so the charge gained or lost is a whole number of electrons, q=ne. Each electron has mass m_e=9.109\times10^{-31}\,\mathrm{kg} (Table 15.1). The mass change is therefore \Delta m=n\,m_e, and eliminating n gives the relationship:
The mass change is directly proportional to the magnitude of the charge. Gaining electrons increases the mass and losing electrons decreases it.
To judge its significance, take a fairly large static charge of 1\,\mu\mathrm{C}. The number of electrons moved is n=\dfrac{1\times10^{-6}}{1.6\times10^{-19}}=6.25\times10^{12}, so
A metal object of about 1\,\mathrm{g}=1\times10^{-3}\,\mathrm{kg} changes by a fraction of about 10^{-15}. The change is far too small to measure, so it is not significant: charging changes the distribution of electrons, not the mass of the object in any practical sense.
Friction between the moving fuel, the hoses and the tanker, and the air, charges the truck and the fuel. A grounding (earthing) cable or chain connects the metal body of the truck to the earth. It gives the excess charge a conducting path, so charge flows away as soon as it forms and the truck stays at the potential of the ground.
Without grounding, charge keeps building up on the metal body. When the field near the surface becomes strong enough, the air ionizes and a spark jumps to the nearby metal. Sudden movement of charge in a spark is the discharge described in Section 15.3, and a spark near flammable fuel vapour can cause a fire or explosion. Grounding removes the cause of the spark.
Protons are held tightly in the nucleus, and neutrons, which have no charge, are also in the nucleus. The electrons in the outermost orbits are loosely bound, so friction or contact can detach them. Only the electrons move, so the nucleus and its charge stay the same.
In a circuit, current in a metal wire is the movement of free electrons, so wires are made of conductors and are covered with insulators (plastic or rubber) so that charge stays in the conductor. In devices, metal casings are earthed so that static charge drains away, and sensitive electronic parts are protected so that a sudden spark does not damage them.
The rubbed balloon carries a net negative charge. Near the wall its field pushes the negative charges of the wall's molecules away and pulls the positive charges closer. The side of the wall facing the balloon becomes slightly positive, so the balloon attracts the wall even though the wall is neutral overall. This induced polarization gives a net attraction, which is why the balloon sticks.
Conductor
In a conductor the electrons are free to move through the material. The balloon draws free electrons away from the near surface and leaves a positive induced charge there. The charge redistributes easily, so the attraction is strong.
Insulator
In an insulator the electrons are firmly bound to their atoms, so they cannot move through the material. Only a slight separation of charge occurs within each molecule (polarization). The attraction is weaker, acts only over a small region near the balloon, and disappears when the balloon is removed.
The direction of the electric field is defined as the direction of the force on a positive test charge. A positive charge placed in a field is therefore pushed in the direction of the field, from a positive source towards a negative source.
A negative charge is pushed in the opposite direction, because the force on it is reversed. For the same field, a positive and a negative charge of equal size experience forces of equal magnitude, F=|q|E, but in opposite directions.
A capacitor has two parallel plates carrying opposite charges. Between the plates the field is uniform, with the same strength and direction at every point (Figure 15.18).
Direction. Reversing the battery connection reverses the charge on each plate and so reverses the field. A positive charge between the plates is then pushed the other way, and a negative charge is pushed the opposite way.
Strength. A stronger field gives a larger force F=qE on a charge placed in it, so a charged particle accelerates more. The field becomes stronger when more charge is placed on the plates.
Both are regions around a source where a body experiences a force. An electric field is produced by a charge and acts on a charge; a gravitational field is produced by a mass and acts on a mass.
- Strength: the electric force between charged particles is far stronger than the gravitational force between their masses. A small static charge can hold light objects, such as paper against a charged comb (Figure 15.10), against their weight.
- Range: both fields decrease with distance by the inverse square law and extend, in theory, to infinity. The field becomes weaker with distance but never becomes zero.
- Forces: gravity is always attractive. Electric forces can be attractive (unlike charges) or repulsive (like charges).
Situations where both act: a charged object near the Earth feels its weight (gravity) and the electric force together. For a small charged particle the electric force is usually much larger than its weight, so the electric force decides its motion. For a large neutral object there is no electric force, and only gravity acts.
Induction moves free charges within an object. An insulator has no free electrons, so a charged object brought near it causes only a slight separation of charge (polarization). When the charged object is removed, the insulator returns to neutral. So an insulator cannot be given a net charge by induction in the way a conductor can.
Conditions. Induction leaves a net charge only on a conductor, which is separated or earthed while the inducing charge is nearby. An insulator is charged only when charge is placed on it directly.
Alternative methods. An insulator is charged by friction, for example by rubbing a plastic rod with wool or fur, or by contact with a charged object. In both cases the charge is transferred to the area of contact and stays there, which is why only that part of the insulator is charged (Figure 15.5 b).
Corona discharge is a faint glow, caused by the local ionization of air, that forms around a conductor when the electric field near its surface is very strong.
Charge on a conductor spreads over the surface and collects most where the surface is most curved. A sharp point therefore carries a high charge density, and the electric field is strongest there. The air close to the point is ionized first, and the ions and electrons formed glow faintly. Corona discharge is seen around high-voltage power lines (Figure 15.21) and during thunderstorms.
At a sharp point the field is so strong that it removes electrons from the surrounding air molecules. This is ionization: each molecule that loses an electron becomes a positive ion. The freed electrons can collide with other atoms and ionize them too, so the ionization can spread as an avalanche.
Uses. The charged air is used in the electrostatic precipitator: dust particles pick up charge and are attracted to a collecting plate, which removes them from the smoke (Figure 15.19). In a photocopier, a corotron sprays charge onto the drum (Figure 15.20).
Problems. Corona discharge on high-voltage lines wastes energy and produces noise. Strong discharges can break down insulation, damage equipment and start fires.
Lichtenberg figures are formed on an insulator, such as acrylic or glass, when a high-voltage discharge passes through its surface. The discharge spreads in a branching path, and the insulating material keeps the tree-like pattern permanently.
They do not appear after every strike because the conditions must all be met: the discharge must pass over or through an insulating surface, and its voltage must be high enough to break down that surface. Most lightning travels through air, trees, buildings and the ground, which are either conductors or do not record the path, so no pattern is left.
Note. The question assumes Lichtenberg figures follow lightning strikes. Section 15.7.1 of the book describes them as made by a high-voltage discharge on an insulator, so the answer treats them as a special case of such a discharge, not as the usual result of a strike.
A lightning rod is a pointed metal rod fixed to the highest point of a building. It is connected by a thick metal conductor to a rod buried in the earth (Figure 15.23). It gives the lightning current a safe, low-resistance path to the ground, so the discharge does not pass through the building.
The point. The electric field is strongest at a sharp point. As the step leader approaches from the cloud, the field at the tip makes positive charges spark out of the rod (a streamer). When the streamer meets the step leader, a conducting path is completed and the lightning strikes the rod. The point therefore attracts the discharge to the rod.
The large current flows down the conductor into the earth and is dispersed there, so the building is not damaged. A lightning rod does not stop lightning; it controls where the strike hits.
Good protection depends on the following points:
- Height: the rod should be the highest point of the building, so that it is the nearest conductor to the negative charge in the cloud.
- Point: a sharp tip gives the strongest field and makes the discharge reliably attach to the rod.
- Conductor: use a good metal with a thick, short and straight path to the ground, avoiding sharp bends, so the current meets little resistance.
- Earth connection: bury the rod in damp soil, or use several earthing rods, so that the charge spreads into the ground and the connection stays effective.
- Coverage: place rods at the corners and the high points of a large building, because one rod protects only the area near it.
- Maintenance: check the joints regularly so that they stay tight and free from corrosion.
Long response questionsp. 183
Electrification
Electrification is the process by which an object acquires an electric charge. A neutral object becomes negative by gaining electrons and positive by losing them. It can be charged by friction, contact or induction, and in each case charge is transferred from one body to another, not created.
Conservation of charge
In an isolated system the total electric charge stays constant. When a glass rod is rubbed with silk, electrons move from the glass to the silk: the glass becomes positive and the silk negative. The gain on one body equals the loss on the other, so the total charge is zero before and after.
Quantization of charge
Charge exists in whole units of the electron charge, e=1.6\times10^{-19}\,\mathrm{C} (Table 15.1). The electron carries charge -e and the proton +e. The net charge of a body is therefore:
For example, a charge of 1\,\mu\mathrm{C} corresponds to n=6.25\times10^{12} electrons. Charge can change only in steps of 1.6\times10^{-19}\,\mathrm{C}, never in smaller amounts.
How these laws govern particles in electronics
In a copper wire, the current is the flow of free electrons. Conservation of charge means that the electrons leaving one part of a circuit must arrive at another part, so the current is the same at every point of a single wire. Quantization means that the current is the rate at which whole electrons move past a point.
A static spark when touching a metal part of an electronic device is the same process on a small scale: electrons move in discrete units, and the spark carries away the charge stored on the body. Designers of electronics therefore earth metal casings and keep sensitive parts away from sudden discharges.
Triboelectric effect (charging by friction)
The triboelectric effect is charging by rubbing: two different materials exchange electrons when they are pressed and rubbed together. The material that holds its electrons less tightly loses them and becomes positive, and the other material gains them and becomes negative. Which material gains electrons depends on the ionization energy and electron affinity of the materials (Section 15.3.1).
For example, a glass rod rubbed with silk becomes positive and the silk becomes negative. A rubber rod rubbed with animal fur becomes negative and the fur becomes positive. Both objects are charged, and their charges are equal and opposite.
Behaviour in contact with conductors
When a charged object touches a conductor, charge flows between them until both are at the same potential. A negatively charged object gives some of its excess electrons to the conductor, so the conductor also becomes negative, and the object keeps a smaller charge.
The charge then spreads over the conductor. On a sphere it spreads evenly over the surface. On an irregular conductor it collects at the more pointed areas (Figure 15.5 a). Both bodies now carry like charges, so they repel each other.
Total charge is conserved throughout: the charge that the conductor gains is exactly the charge the object loses.
Electrons in conductors
In a conductor the valence electrons, which are the electrons in the outermost orbits, are loosely bound to their atoms. They detach easily and move freely through the metal, forming a sea of free electrons (Figure 15.4 a). This is why charge spreads over a conductor and why current can flow in it.
Electrons in insulators
In an insulator, even the least tightly bound electrons are firmly attached to their atoms. They cannot move through the material, so charge stays where it was placed (Figure 15.4 b).
Comparison
| Property | Conductor | Insulator |
|---|---|---|
| Outer electrons | loosely bound | tightly bound |
| Free electrons | many, free to move | none that move through the material |
| Charge placed on it | spreads over the whole surface | stays where it was placed |
| Typical examples | copper, aluminium, metals | rubber, glass, plastic, wood |
Practical uses
Conductors carry current in wires and are used in electrical contacts and earthing rods, because charge moves through them easily. Insulators cover wires, plugs and the handles of tools, so that charge cannot reach the user, and they support the conductors on poles and towers.
Comparison of the methods
| Method | Needs contact? | Works best on | Result on the object |
|---|---|---|---|
| Friction | Yes, by rubbing | insulators | Both bodies charged with opposite signs |
| Conduction | Yes, touching | conductors | Object takes the same sign as the charged body |
| Induction | No | conductors | Charge of opposite sign on the near side; object charged oppositely once separated |
Friction
Friction charges insulators very effectively, because the charge stays where it is produced. It is unreliable for metals: a metal rubbed in the hand leaks its charge away to the body and the ground unless it is insulated. The amount of charge depends on the materials and the surfaces, so the results vary from one rubbing to the next. Examples are the static of a car seat and hair lifting after brushing (Section 15.1).
Conduction
A conductor touched by a charged object takes on the same sign of charge, and the charge is shared between the two. The method is efficient for metals because the charge spreads through them quickly. It is not effective for insulators, which keep the charge only at the point of touching.
Induction
A charged object placed near a conductor separates its charge without any contact. Induction is efficient for conductors because their free electrons move easily. For insulators it is ineffective, because they only polarize slightly and no net charge is left behind.
Evaluation
For metal objects, induction followed by earthing is the most controlled method: the size of the charge is set by the inducing object, and the source charge is not used up. For glass and plastics, friction is the only practical method, but its result is hard to control. Conduction is quick and effective for metals, but it gives the object the same sign as the source, and it cannot be used to charge insulators.
Applications include the charging of an electroscope by induction (Figure 15.13) and the electropainting of car bodies, where the body and the paint are given opposite charges so that the paint spreads evenly (Science Tidbits).
Procedure
- Set up two metal spheres X and Y on insulating stands, touching each other so that they act as one conductor.
- Bring a negatively charged rubber strip close to sphere X without touching it. Electrons are repelled to the far side, so X becomes positive on its near side and Y negative on its far side. This is induction.
- While the strip is still nearby, separate the spheres by moving them apart on their stands. The induced charges are now held on separate spheres.
- Remove the strip. The spheres keep their charges, X positive and Y negative, because the charges cannot return while the spheres are apart.
- Check the result with an electroscope that carries a known charge. The leaves diverge when the sphere carries charge, and the sign is found from the method in Section 15.4.
Real-world uses of induction
- Electroscope: a charged rod induces charge on the metal disc and leaves, and the leaves diverge (Section 15.4).
- Electrostatic precipitator: dust particles are charged and attracted to collecting plates, which removes them from smoke (Section 15.6.1).
- Photocopier and laser printer: the drum is charged and the image is formed by the charge it carries (Section 15.6.2).
- Electropainting: the body and the paint are given opposite charges so that the paint is attracted evenly to the car (Science Tidbits).
Electric field
The electric field at a point is the force per unit positive test charge placed there:
Its direction is the direction of the force on a positive test charge, and its SI unit is N/C.
What field lines show
Field lines start on positive charges and end on negative charges (Figure 15.15). The direction of a line at any point is the direction of the field there. The density of the lines shows the strength: where the lines are close together the field is strong, and where they are far apart it is weak.
Inverse square law
The field of a point charge weakens with distance. Doubling the distance reduces the field to one quarter of its value, which is the inverse square law. The graph shows this relation.
Parallel plates and capacitors
Between two oppositely charged parallel plates the field lines are straight, parallel and equally spaced, so the field is uniform (Figure 15.18). A charged particle between the plates therefore feels the same force at every point, which makes the parallel plates of a capacitor predictable.
Shielding
A charged conductor has zero field inside it, because its charge spreads over the surface and the field inside cancels out (Figure 15.17 for a sphere). A metal enclosure therefore shields what lies inside it from outside electric fields, which is why sensitive electronic equipment is placed in metal boxes.
How an electroscope works
A gold-leaf electroscope has a metal disc at the top of a metal rod. The rod ends in two thin gold leaves inside a housing that insulates them from the surroundings (Figure 15.11). The leaves hang together when the electroscope is neutral.
When a charged object touches the disc, charge spreads over the disc, rod and leaves. The leaves get like charges, which repel each other, so they diverge. The more charge there is, the wider the leaves open. An electroscope shows that an object is charged, and it gives the sign of the charge only when a known charge is first given to it (Figure 15.12).
Improvements for detecting weaker charges
- Lighter leaves: use thinner, lighter leaves, so that the repulsion of a small charge is enough to move them.
- Longer leaves: longer leaves swing through a larger angle for the same charge, so the movement is easier to see.
- Dry and clean insulation: keep the instrument dry and clean, because moisture and dust give the charge a path to leak away (Section 15.3.4).
- Enclosed housing: keep the leaves inside a closed housing, which stops draughts from moving them.
- Larger disc: a larger disc collects more of a weak charge and gives a bigger response.
- Scale: fit a scale behind the leaves, so that small deflections can be read accurately.
Electrostatic precipitator
Smoke enters across a negatively charged metal grid, and the dust particles pick up negative charge there. The charged particles are then attracted to a positively charged collecting plate, where they stick, and the cleaned gas leaves the chimney (Figure 15.19). The dust builds up on the plates and is removed from time to time.
To improve it: use a steady high voltage only as strong as needed, so that particles are charged and attracted without wasting energy; increase the area of the collecting plates, so that more particles are caught on each pass; and clean the plates regularly, because a layer of dust reduces the field and the attraction.
Photocopier
A photocopier uses xerography. A corotron charges the selenium drum, light from the original removes the charge from the white areas, and the charged image attracts negatively charged toner. The toner is then transferred to paper and fused by heat and pressure (Section 15.6.2 and Figure 15.20).
To improve it: write the image with a laser, which gives a precise charged image and less wasted light (Science Tidbits); charge the drum only over the area needed; keep the drum and toner clean so that toner sticks only to the charged image; and fuse at the lowest temperature that gives a good copy, which saves the energy spent heating the paper.
Note. Figure 15.19 and the text of the book disagree. The text says the smoke particles become positive and are attracted to a negatively charged mesh, but the figure shows them picking up negative charge and collecting on the positively charged plate. The figure is the consistent version, and the answer follows it.
How electric breakdown occurs
An insulator normally blocks the flow of charge. When the electric field becomes strong enough, electrons are pulled out of their atoms and the material conducts. This is electrical breakdown. In a gas such as air, a strong field ionizes the gas atoms; the freed electrons collide with other atoms and cause more ionization, in an avalanche effect (Section 15.7).
Corona discharge around sharp points (Figure 15.21) and Lichtenberg figures left on insulators (Figure 15.22) are visible signs of breakdown.
Conditions that make breakdown likely
- Sharp points or edges, where the field is concentrated (Section 15.7.1).
- High voltage, which produces a strong field across the insulation.
- Damp or dirty surfaces, where water films let charge move over an insulator (Section 15.3.4).
- Damaged insulation, where cracks or thin spots raise the local field.
Safety measures for high-voltage environments
- Use insulation of high breakdown strength and sufficient thickness, so that the field stays below the value needed for breakdown.
- Round off sharp metal edges and fit smooth caps, so that the field does not concentrate and corona does not start.
- Keep high-voltage parts at a safe distance, enclose them and fit barriers, so that people cannot touch them.
- Earth all metal casings and frames, so that stray charge drains away and a person touching them is at zero potential.
- Keep insulators clean and dry, because damp or dirty surfaces let charge leak across them.
- Use warning signs and trained staff, and inspect the insulation regularly for cracks.
Production of lightning
Collisions between air, water droplets and other particles inside a storm cloud separate charge. Positive charge rises to the top of the cloud and negative charge sinks to its base (Section 15.7.2). The negative base of the cloud induces a positive charge on the ground below.
- The strong field at the base of the cloud ionizes the air, and a step leader, a zigzag path of negative charge, moves down towards the ground.
- A streamer of positive charge rises from the ground or from a raised object to meet the step leader.
- When they meet, a conducting path is complete and the negative charge rushes down to the ground at up to 100{,}000\,\mathrm{km\,s^{-1}}.
How a lightning rod works
A lightning rod is a pointed metal rod on the highest point of a building, joined by a metal conductor to a rod buried in the earth (Figure 15.23). The field is strongest at the point, so a streamer forms there first and joins the step leader. The strike therefore hits the rod, and its large current flows safely into the earth instead of through the building.
Additional safety measures in lightning-prone areas
- Shelter in a sturdy building during a storm, and keep away from doors and windows.
- If there is no shelter, avoid open fields, water and tall isolated objects, and crouch with the feet together (Section 15.7.4).
- Fit lightning rods to tall buildings, masts and towers, each with a short, low-resistance path to the earth, and check the joints regularly.
- Earth the electrical systems of buildings and fit surge protectors to sensitive electronics, so that a surge from a strike is diverted to the ground.
- Use a storm warning and suspend outdoor work, sports and work on towers while thunder can be heard.
Numerical response questionsp. 183–184
- q_0 = 3.0\times10^{-5}\,\mathrm{C} 30 \mu C
- F_E = 0.600\,\mathrm{N} force on the test charge
- E, the magnitude of the field
- The field is the force per unit positive test charge.E=\dfrac{F_E}{q_0}
- Substitute, writing 30\,\mu\mathrm{C} as 3.0\times10^{-5}\,\mathrm{C}.E=\dfrac{0.600}{3.0\times10^{-5}}
- Evaluate.E=2.0\times10^{4}\,\mathrm{N\,C^{-1}}
Book answer. 2.00\times10^{4}\,\mathrm{N/C}
- q = -1.0\times10^{-6}\,\mathrm{C} negative charge
- E = 1.7\times10^{6}\,\mathrm{N\,C^{-1}} to the right
- F (magnitude and direction)
- The force on a charge in a field is F=qE. Use the magnitudes first.F=|q|E
- Substitute.F=1.0\times10^{-6}\times1.7\times10^{6}=1.7\,\mathrm{N}
- The charge is negative, so the force is opposite to the field. The field points right, so the force points left.
- q = +1.0\times10^{-6}\,\mathrm{C} positive charge
- E = 2\times1.7\times10^{6}=3.4\times10^{6}\,\mathrm{N\,C^{-1}} doubled field, to the right
- F (magnitude and direction)
- Double the field.E=2\times1.7\times10^{6}=3.4\times10^{6}\,\mathrm{N\,C^{-1}}
- Find the force on the positive charge.F=qE=1.0\times10^{-6}\times3.4\times10^{6}=3.4\,\mathrm{N}
- The charge is positive, so the force is in the direction of the field, to the right.
Book answer. 1.7 N [left], 3.4 N [right]
- F_E = 0.5\,\mathrm{N} force on the test charge
- E = 2.0\,\mathrm{N\,C^{-1}} field
- q_0, the magnitude of the test charge
- The field is E=F_E/q_0, so the charge is q_0=F_E/E.q_0=\dfrac{F_E}{E}
- Substitute the values.q_0=\dfrac{0.5}{2.0}
- Evaluate.q_0=0.25\,\mathrm{C}
Book answer. 0.25\,\mathrm{C}
- q = 3.0\,\mu\mathrm{C}=3.0\times10^{-6}\,\mathrm{C} charge
- E = 1.5\,\mathrm{N\,C^{-1}} uniform field
- F, the force on the charge
- Rearrange E=F/q to give the force: F=qE.F=qE
- Substitute.F=3.0\times10^{-6}\times1.5
- Evaluate.F=4.5\times10^{-6}\,\mathrm{N}=4.5\,\mu\mathrm{N}
Book answer. 4.5\,\mu\mathrm{N}
- F_E = 0.01\,\mathrm{N} force on the electron
- q = 1.6\times10^{-19}\,\mathrm{C} charge of an electron, magnitude
- E, the field strength
- The field is the force per unit charge: E=F_E/|q|.E=\dfrac{F_E}{|q|}
- Substitute.E=\dfrac{0.01}{1.6\times10^{-19}}
- Evaluate.E=6.25\times10^{16}\,\mathrm{N\,C^{-1}}
Book answer. 6.25\times10^{16}\,\mathrm{N/C}
Note. The electron is negative, so the force on it points opposite to the field. The sign of the charge gives only the direction of the field; the magnitude of the field is found from the magnitude of the charge.
- q = 1.6\times10^{-19}\,\mathrm{C} charge of an electron, magnitude
- E = 20\,\mathrm{N\,C^{-1}} uniform field
- F, the magnitude of the force
- The force on a charge in a field is F=|q|E. Being released from rest gives the electron zero speed at the start, but the force depends only on its charge and the field.F=|q|E
- Substitute.F=1.6\times10^{-19}\times20
- Evaluate.F=3.2\times10^{-18}\,\mathrm{N}
Book answer. 3.2\times10^{-18}\,\mathrm{N}
FBISE 2026 questions
Questions from the FBISE SSC-II 2026 (1st Annual) papers that belong to this unit, answered the way an examiner expects.
- AAtoms
- BProtons
- CNeutrons
- DElectronsAnswer
When two different materials are rubbed together, the loosely held outer electrons pass from the material whose atoms hold them less strongly to the one that attracts them more strongly (section 15.3.1). The material that loses electrons becomes positive and the one that gains them becomes negative.
Protons and neutrons are bound inside the nucleus and are not removed by rubbing, so B and C are wrong. Whole atoms (A) are not transferred either; only electrons move.
Electric field (1 mark)
An electric field is the region around a charge in which it exerts a force on other charges. The charges do not have to touch: any charge brought into the region feels a force.
Its strength is measured by the electric field intensity E, the force per unit positive test charge, E=\dfrac{F}{q_0}, with SI unit \mathrm{N\,C^{-1}}.
Effect on a test charge (2 marks)
Rearranging E=F/q_0 gives the force on a charge q placed in a field of strength E:
- A positive test charge feels a force of size qE in the same direction as the field. It is pushed along the field, away from a positive source charge and towards a negative one.
- A negative test charge feels a force of the same size in the opposite direction to the field.
- The test charge does not have to touch the source charge, and the force is larger where the field is stronger (nearer the source).
An insulator has no free electrons, so a charge placed on it cannot leak away through the material. Exposing it to moist (humid) air discharges it (section 15.3.4).
Water molecules in damp air stick to the surface of the insulator. They are polar molecules, so they interact with the charged areas and form a thin conducting layer of water on the surface. The charge can now move along this layer and escape, so the insulator is discharged.
The ions present in humid air also help: they are attracted to the charged surface and neutralise the static charge on it. This is why static electricity is much more noticeable on dry days than on humid ones.
- ANegative chargeAnswer
- BPositive charge
- CNeutral charge
- DBoth charges
Only the loosely bound outer electrons move when two materials are rubbed, and electrons carry negative charge. The material that loses electrons becomes positive and the one that gains them becomes negative (section 15.3.1).
Option B is the tempting one because one body ends up positive, but that is only because it has lost electrons. The protons stay fixed in the nuclei, so positive charge is not transferred. A neutral charge (C) does not exist, and D is wrong because only one type moves.
Electric field (1 mark)
An electric field is the region around a charge in which it exerts a force on other charges. The charges do not have to touch: any charge brought into the region feels a force.
Its strength is measured by the electric field intensity E, the force per unit positive test charge, E=\dfrac{F}{q_0}, with SI unit \mathrm{N\,C^{-1}}.
Positive test charge in the field (2 marks)
The direction of the electric field at a point is defined as the direction of the force on a positive test charge placed there. So a positive test charge placed in an electric field feels a force F=qE in the same direction as the field.
It is pushed along the field: away from a positive source charge (repelled) and towards a negative source charge (attracted). The force is larger where the field is stronger, that is, closer to the source charge, since the field of a point charge falls off with distance as an inverse square law.
An insulator cannot lose its charge through its own material because it has no free electrons. Holding it over a flame changes its surroundings so that the charge can be neutralised (section 15.3.4).
The heat of the flame excites electrons and ionises the air around the insulator, so the air becomes conducting. Ions of the opposite sign are attracted to the charged surface and neutralise the static charge on it.
The heat also temporarily increases the surface conductivity of the insulator, so the static charges can move and escape from it. In this way the insulator is discharged.
- AGains neutrons
- BLoses electrons
- CGains protons
- DGains electronsAnswer
An object is negatively charged when it has more electrons than protons. Since the protons stay in the nucleus, this happens only when the object gains electrons.
Option B is the tempting wrong choice: losing electrons leaves more protons than electrons, so the object becomes positive. Neutrons (A) are neutral, and protons (C) are positive and cannot be added by charging, so they could not make the object negative.
Electric field (1 mark)
An electric field is the region around a charge in which it exerts a force on other charges. The charges do not have to touch: any charge brought into the region feels a force.
Its strength is measured by the electric field intensity E, the force per unit positive test charge, E=\dfrac{F}{q_0}, with SI unit \mathrm{N\,C^{-1}}.
Two characteristics (2 marks)
- It is a vector quantity. The electric field intensity E=F/q_0 has both magnitude and direction. Its direction at a point is the direction of the force on a positive test charge placed there, and its SI unit is \mathrm{N\,C^{-1}}.
- Its strength decreases with distance from the source charge, following an inverse square law for a point charge. If the strength is E_0 at distance r_0, it is \tfrac14E_0 at 2r_0.
(Other correct points: a positive charge in the field is pushed along the field and a negative charge against it, with force F=qE; and the field does not depend on the size of the test charge.)
Charge on an insulator cannot flow through it, because an insulator has no free electrons. Heating changes the insulator and the air around it so that the charge can escape (section 15.3.4).
- The heat excites the electrons and ionises the surrounding air, which makes the air conducting. Opposite ions in the air are attracted to the charged surface and neutralise it.
- The heat also increases the surface conductivity of the insulator for a short time, so the static charges can move and discharge.
Therefore holding a charged insulator over a flame discharges it.
Exam focus
- What is an electric field? Define electric field intensity, give its unit and direction, and state the force on a positive and a negative test charge, F=qE. (short)Asked as Q.2 (ii) (3 marks, 1+2) in all three 2026 sets: B (effect on a test charge), D (positive test charge) and M (two characteristics). The surest short question of the unit.Go to answer
- Explain how a charged insulator is discharged: by heating over a flame and by moist air. (short)Q.2 (vii) OR (3 marks) in all three 2026 sets: moisture in Set B, flame in Set D, heating in Set M. Section 15.3.4 gives both methods.Go to answer
- Which particles are transferred when solids are charged by friction? Say what makes an object positive or negative. (mcq)MCQ 3 in all three 2026 sets: electrons (Set B), negative charge (Set D), gains electrons (Set M). Also short question 3 of the book.Go to answer
- Calculate the electric field strength, the force on a charge or the test charge from E=F/q_0 and F=qE. (numerical)No numerical from this unit appeared in the 2026 papers, but numerical problems 1 to 6 of the book all use these two relations and the SI unit \mathrm{N\,C^{-1}} is easily asked.Go to answer
- Describe charging by friction, contact and induction, and say whether insulators can be charged by induction. (long)The three methods of charging are the core of the unit and the basis of the friction MCQ in all 2026 sets; comprehensive questions 4 and 5 and short question 8 of the book test them. No long question from this unit appeared in 2026.Go to answer
- How do positive and negative charges behave differently in an electric field? (short)Short question 5 of the book is the same idea as the test-charge part of Q.2 (ii) in Sets B and D of 2026.Go to answer
- Explain how an electroscope detects a charge. (long)Not asked in 2026, but a standard long question of the unit (comprehensive question 7) and the topic of MCQ 1 and MCQ 9 of the book.Go to answer
- Explain how lightning is produced and how a lightning rod protects a building. (long)Not asked in 2026, but comprehensive question 10 and short questions 12 and 13 of the book make it a likely long question.Go to answer