Senior 1 practice book · Unit 7 of 9

Electrostatics

50 questions that complete the Senior 1 quiz for this unit: 28 core and 22 challenge. Easy and hard questions are mixed. Try each question, then tap “Show answer”.

Common misconceptions

A body becomes positive by gaining positive charges (protons).Protons are fixed in the nucleus. A body becomes positive by LOSING electrons, and negative by gaining them.
If two objects attract each other, both must be charged with opposite charges.A charged object also attracts a neutral object by induction, so attraction does not prove both are charged. Only repulsion proves that both carry the same kind of charge.
A bigger charge pushes a smaller charge harder than the small charge pushes back.The forces on the two charges are equal in size and opposite in direction (Newton's third law), whatever the sizes of the charges.
Charge spreads evenly over any charged conductor.Charge sits on the outside surface of a conductor and crowds together where the surface is most sharply curved, such as at points and edges.

What this unit covers

Topics marked new are not tested much in the quiz, so this book gives them extra questions.

Structure of the atom and the origin of electric charge
Charging by friction (rubbing) and electron transfer
Charging by contact (conduction) and sharing of charge
Charging by induction
Laws of electrostatics and testing whether a body is charged
Coulomb's law: calculations and proportional reasoning
Quantisation of charge: Q = ne
Conductors and insulators
Gold-leaf electroscope and its uses
Electric field and electric field-line patterns
Distribution of charge on conductors and action at points
Uses of static electricity: spray painting, crop spraying, dust precipitators, photocopiers
Hazards of static electricity and protection from lightning

Go to the questions

Questions (1–50)

Easier and harder questions are mixed, just like in a real exam. The 22 harder ones are marked ★ Challenge.

1True or false
Neutrons carry a small negative charge.
Show answer
Answer: False
Neutrons have no charge; only protons (+) and electrons (−) are charged.
Common mistakeLearners sometimes mix up 'neutral' and 'negative'; the neutron is neutral.
2Multiple choice · ★ Challenge
Which observation PROVES that a plastic rod is charged?
1. AIt attracts small pieces of dry paper lying on a desk
2. BIt repels a small ball that is known to be charged
3. CIt attracts a negatively charged ball on a thread
4. DIt attracts a light, uncharged metal-coated ball
Show answer
Answer: B. It repels a small ball that is known to be charged
A charged rod can attract neutral objects by induction, so attraction proves nothing on its own; only repulsion shows both objects carry like charges.
Common mistakeChoosing 'attracts small pieces of paper' is tempting, but a charged rod attracts neutral paper, and the test does not show the rod's charge for certain.
3True or false
Electric field lines can cross each other.
Show answer
Answer: False
At any point the field has only one direction, so two lines can never cross.
Common mistakeLearners draw crossing lines when sketching two charges; if lines crossed, a charge there would have two force directions at once.
4Multiple choice · ★ Challenge
Charge leaks quickly into the air from a sharp point on a charged conductor (point action) because:
1. AThe point gets hot from the charge, and the hot metal boils off its electrons
2. BThe point is thinner, so the electrons are squeezed out of the metal by pressure
3. CThe strong field at the point ionises the air, and the ions carry charge away
4. DThe point is closer to the earth, so charge falls straight to the ground below
Show answer
Answer: C. The strong field at the point ionises the air, and the ions carry charge away
Crowded charge at a point gives a strong field that ionises air molecules; ions of opposite sign are drawn to the point and neutralise it, while like ions are repelled away.
Common mistakeChoosing 'the point gets hot' invents a heating effect; point action is due to the strong electric field, not heat.
5True or false
Damp air makes it harder for objects to stay charged.
Show answer
Answer: True
Moist air and a thin film of water on surfaces conduct slightly, so charge leaks away; static experiments work best on dry days.
Common mistakeSome learners think water 'adds charge'; it actually lets charge leak away.
6True or false
On a charged hollow metal sphere, all the charge sits on the outside surface.
Show answer
Answer: True
Like charges repel and spread as far apart as possible, so they settle on the outer surface; the inside has no charge.
Common mistakeLearners imagine charge filling a conductor like water in a tank; in a conductor it stays on the outer surface.
7Multiple choice · ★ Challenge
In electrostatic crop spraying, all the droplets are given the same charge as they leave the nozzle. This makes them:
1. AAttract each other and join into large heavy drops
2. BLose their pesticide and become harmless to insects
3. CFall straight down without any effect from the wind
4. DRepel each other and spread into a fine, even cloud
Show answer
Answer: D. Repel each other and spread into a fine, even cloud
Like charges repel, so the droplets spread apart evenly; they are also attracted to the plants (by induction), so they wrap around the leaves.
Common mistakeChoosing 'attract each other' forgets that like charges repel.
8True or false
A rubbed balloon sticks to a neutral wall because the wall stores the opposite charge permanently.
Show answer
Answer: False
The balloon induces opposite charge on the near surface of the wall; the wall as a whole stays neutral and the effect disappears when the balloon is removed.
Common mistakeLearners think the wall must already be charged; the attraction comes from charge induced (separated) by the balloon.
9Multiple choice · ★ Challenge
A charged electroscope is left alone in a cupboard. Over several hours its leaf slowly falls. The most likely reason is that:
1. AThe gold leaf becomes heavier as it collects dust
2. BCharge leaks away through moist air and the support
3. CProtons slowly move up from the leaf to the cap
4. DThe charge is used up by keeping the leaf raised
Show answer
Answer: B. Charge leaks away through moist air and the support
No insulator is perfect; moisture in the air and on the plastic support lets the charge leak away slowly, so the leaf falls.
Common mistakeChoosing 'the charge is used up' treats charge like fuel; holding the leaf up needs no energy, and charge only leaves by leaking.
10True or false
Electrostatic crop sprayers can make pesticide droplets coat the undersides of leaves as well as the tops.
Show answer
Answer: True
Charged droplets are attracted to the plant from all sides, so they wrap around the leaves and less pesticide is wasted.
Common mistakeSome learners think sprays can only land where they fall by gravity; electrostatic attraction pulls droplets onto hidden surfaces.
11Multiple choice · ★ Challenge
A small NEGATIVE charge is placed in an electric field whose lines point to the right. In which direction is the force on it?
1. ATo the right, along the field lines
2. BUpwards, at right angles to the lines
3. CThere is no force on a negative charge
4. DTo the left, opposite to the field lines
Show answer
Answer: D. To the left, opposite to the field lines
Field lines show the force on a positive charge; a negative charge feels a force in the opposite direction, to the left.
Common mistakeChoosing 'to the right' applies the field direction to every charge; it is only the direction of the force on a positive charge.
12True or false
A car with a metal body is a fairly safe place in a thunderstorm, because a lightning current flows over the outside of the metal body to the ground.
Show answer
Answer: True
Charge on a conductor stays on its outside surface, so the current passes round the metal shell and the people inside are protected (the rubber tyres are not the reason).
Common mistakeMany people believe the rubber tyres protect the car; a lightning flash easily crosses a few centimetres of rubber, so it is the metal shell that protects.
13Multiple choice · ★ Challenge
Two parallel metal plates are connected to a battery, one positive and one negative. The field between them (away from the edges) is shown by:
1. ACurved lines that bulge outwards from the middle of each plate
2. BParallel, evenly spaced lines from the + plate to the − plate
3. CLines from the − plate to the + plate, crowded near the middle
4. DCircles centred on the middle of the space between the plates
Show answer
Answer: B. Parallel, evenly spaced lines from the + plate to the − plate
Between parallel plates the field is uniform: the same strength and direction everywhere, so lines are parallel, equally spaced and run from + to −.
Common mistakeChoosing lines from − to + reverses the convention; field lines always start on positive charge and end on negative charge.
14Fill in the blank
The positively charged particles found in the nucleus of an atom are called ______.
Show answer
Answer: protons
The nucleus contains protons (positive) and neutrons (no charge); electrons orbit outside it.
Common mistakeWriting 'neutrons' is a common slip; neutrons are in the nucleus but carry no charge.
15Fill in the blank
Materials such as rubber, glass and dry wood, in which electrons are not free to move, are called ______.
Show answer
Answer: insulators
Insulators hold their electrons tightly, so charge does not flow through them.
Common mistakeWriting 'semiconductors' is incorrect at this level; rubber and glass are good insulators.
16Multiple choice · ★ Challenge
A positively charged rod is held near one end of an uncharged metal bar on an insulating stand. The rod is then taken away; the bar was never earthed or touched. The bar is now:
1. ANegatively charged, because electrons were attracted to it
2. BPositively charged, the same sign as the rod held near it
3. CCharged both ways, positive at one end and negative at the other
4. DUncharged, because its free electrons spread out evenly again
Show answer
Answer: D. Uncharged, because its free electrons spread out evenly again
The rod only separated the bar's charges. With no earth connection, no charge entered or left, so when the rod goes the electrons spread back and the bar is neutral.
Common mistakeChoosing 'negatively charged' forgets that charging by induction needs earthing while the rod is near; without it, the separation is undone.
17Fill in the blank · ★ Challenge
A small metal ball carrying +12 nC is touched against an identical uncharged ball, and then against a second identical uncharged ball. The first ball now carries ______ nC.
Show answer
Answer: +3 (3)
First touch: 12 ÷ 2 = 6 nC each. Second touch: 6 ÷ 2 = 3 nC each.
Common mistakeWriting +4 nC shares 12 nC among three balls at once; the ball shares its charge twice, halving it each time.
18Multiple choice
An electric field is:
1. AThe total amount of charge stored on a body
2. BThe flow of electrons along a metal wire
3. CA region in which a charge experiences a force
4. DA region in which a magnet always points north
Show answer
Answer: C. A region in which a charge experiences a force
Any charge placed in an electric field feels an electric force; the field exists around every charged body.
Common mistakeChoosing the magnet option confuses electric fields with magnetic fields, which act on magnets and moving charges.
19True or false
When a large charge and a small charge repel each other, the large charge pushes harder on the small one than the small one pushes on the large one.
Show answer
Answer: False
By Coulomb's law and Newton's third law the two forces are equal in size (F = kq₁q₂/r² is the same for both) and opposite in direction.
Common mistakeLearners link 'bigger charge' with 'bigger push'; the product q₁q₂ is shared, so both feel the same force.
20Multiple choice · ★ Challenge
When an aircraft is refuelled at Kigali International Airport, the plane and the fuel tanker are first connected to earth by a wire. Why?
1. AFlowing fuel can build up charge, and a spark could ignite the vapour
2. BThe wire measures how much fuel has entered the aircraft's fuel tanks
3. CThe wire stops the tanker from rolling away while the fuel is pumped
4. DEarthing makes the fuel flow faster, so refuelling takes less time
Show answer
Answer: A. Flowing fuel can build up charge, and a spark could ignite the vapour
Friction between fuel and hose can charge the plane or tanker; earthing lets the charge flow away safely so no spark jumps near the fuel vapour.
Common mistakeChoosing 'makes the fuel flow faster' is wrong; earthing does not change the flow, it removes charge to prevent sparks.
21Fill in the blank
The escape of charge into the air from sharp points on a charged conductor is called ______ action (or corona discharge).
Show answer
Answer: point
Point action happens because charge density, and so the field, is greatest at sharp points.
Common mistakeWriting 'induction' names a different process; induction separates charge but does not let it leak into the air.
22Multiple choice · ★ Challenge
In a list of materials, those higher up lose electrons more easily: glass (top), wool, silk, polythene (bottom). Wool is rubbed with glass. What happens?
1. AWool loses electrons and becomes positive; glass becomes negative
2. BBoth become negative, because rubbing always adds electrons
3. CWool gains electrons and becomes negative; glass becomes positive
4. DNeither is charged, because both of them are insulators
Show answer
Answer: C. Wool gains electrons and becomes negative; glass becomes positive
Glass is above wool, so glass loses electrons more easily; electrons pass from glass to wool, making wool negative and glass positive.
Common mistakeChoosing 'wool becomes positive' remembers that wool usually charges positive (against polythene); its charge depends on the partner material.
23Fill in the blank
In a dust precipitator, dust particles are given a charge and are then collected on metal plates that carry the ______ charge.
Show answer
Answer: opposite
Opposite charges attract, so oppositely charged plates pull the charged dust out of the gas.
Common mistakeWriting 'same' would make the plates repel the dust, so it would not be collected.
24Multiple choice
The electric field lines around an isolated positive point charge:
1. APoint straight inwards, towards the charge, in all directions
2. BForm closed circles around the charge, like ripples on water
3. CRun parallel to each other, from left to right across the page
4. DPoint straight outwards, away from the charge, all round it
Show answer
Answer: D. Point straight outwards, away from the charge, all round it
Field lines show the direction of the force on a small positive test charge; it is repelled, so lines point radially outwards.
Common mistakeChoosing 'inwards' gives the pattern of a NEGATIVE charge; lines point away from + and towards −.
25Multiple choice · ★ Challenge
A neutral carbon atom has 6 protons. It gains one extra electron (e = 1.6 × 10⁻¹⁹ C). What is its overall charge now?
1. A+1.6 × 10⁻¹⁹ C
2. B−9.6 × 10⁻¹⁹ C
3. C−1.6 × 10⁻¹⁹ C
4. DZero, as the protons do not change
Show answer
Answer: C. −1.6 × 10⁻¹⁹ C
Before, +6e and −6e cancel. With one extra electron the total is +6e − 7e = −e = −1.6 × 10⁻¹⁹ C.
Common mistakeChoosing −9.6 × 10⁻¹⁹ C counts all 6 electrons (6 × 1.6 × 10⁻¹⁹) and forgets that 6 of them are cancelled by the 6 protons; only the extra one counts.
26Multiple choice
An electrostatic precipitator in the chimney of a cement factory is used to:
1. AMake the smoke much hotter so that it rises higher above the factory
2. BProduce electricity for the factory from the moving smoke
3. CAdd charge to the air so that rain falls near the factory
4. DRemove dust from smoke by charging it and catching it on plates
Show answer
Answer: D. Remove dust from smoke by charging it and catching it on plates
Dust particles pass charged wires and pick up charge; they are then attracted to oppositely charged plates and collected, so cleaner gas leaves the chimney.
Common mistakeChoosing 'produce electricity' is a guess from the word 'electrostatic'; the device uses electricity to clean smoke, it does not generate it.
27Short answer · ★ Challenge
Explain how static electricity is used in a photocopier.
Show answer
Model answer: A drum is given a charge. Light reflected from the white parts of the original falls on the drum and removes the charge there, leaving a charged 'image' of the dark parts. Oppositely charged toner powder sticks only to the charged areas. Paper is charged to attract the toner from the drum, and heat then fixes the toner to the paper.
Common mistakeLearners often say 'light charges the drum'; in fact light REMOVES charge from the drum where the page is white.
28Multiple choice
A pear-shaped metal conductor is charged. Where is the charge most concentrated?
1. AAt the widest, most rounded end
2. BEvenly everywhere over its surface
3. CAt the sharpest, most pointed end
4. DInside the metal, at its very centre
Show answer
Answer: C. At the sharpest, most pointed end
Charge crowds where the surface curves most sharply, so the surface charge density is greatest at the pointed end.
Common mistakeChoosing 'evenly everywhere' would only be true for a sphere; on other shapes charge collects at points.
29Multiple choice · ★ Challenge
Which of these charges is IMPOSSIBLE for a small oil drop? (e = 1.6 × 10⁻¹⁹ C)
1. A3.2 × 10⁻¹⁹ C
2. B2.4 × 10⁻¹⁹ C
3. C4.8 × 10⁻¹⁹ C
4. D8.0 × 10⁻¹⁹ C
Show answer
Answer: B. 2.4 × 10⁻¹⁹ C
Charge must be a whole number of electron charges: 3.2 = 2e, 4.8 = 3e, 8.0 = 5e, but 2.4 ÷ 1.6 = 1.5, which is not a whole number.
Common mistakeChoosing the smallest-looking value is a guess; test each one by dividing by 1.6 × 10⁻¹⁹ and look for a whole number.
30Fill in the blank
If the distance between two point charges is reduced to one fifth of its value, the force between them becomes ______ times as large.
Show answer
Answer: 25
F ∝ 1/r²: r → r/5 gives F × 5² = 25F.
Common mistakeWriting 5 forgets to square the distance factor.
31Multiple choice
A negatively charged rod is brought NEAR the cap of a neutral electroscope without touching it. The leaf:
1. AStays down, because the rod does not touch the electroscope
2. BRises, as electrons are repelled down to the leaf and stem
3. CRises, because protons move up from the leaf to the cap
4. DFalls further, because electrons leave through the gold leaf
Show answer
Answer: B. Rises, as electrons are repelled down to the leaf and stem
The negative rod repels free electrons from the cap to the leaf and stem, which both become negative and repel each other.
Common mistakeChoosing 'stays down' assumes charge must be given by contact; induction separates charge even without touching.
32Multiple choice · ★ Challenge
Two identical metal spheres touch and are then separated; each now carries +3 nC. Before touching, one sphere carried +10 nC. What did the other carry?
1. A−4 nC
2. B+4 nC
3. C−7 nC
4. D+13 nC
Show answer
Answer: A. −4 nC
Total charge is conserved: 2 × (+3) = +6 nC. Other sphere = 6 − 10 = −4 nC.
Common mistakeChoosing −7 nC subtracts the final charge of one sphere (3 − 10) and forgets that the total after sharing is 2 × 3 = 6 nC.
33Multiple choice
A negatively charged rod is held near a metal sphere, and the sphere is earthed with a finger. Which way do the electrons flow?
1. AFrom the sphere, through the finger, to earth
2. BFrom the earth, through the finger, onto the sphere
3. CFrom the rod, through the air, onto the sphere
4. DNo electrons move; only protons move to earth
Show answer
Answer: A. From the sphere, through the finger, to earth
The negative rod repels the sphere's free electrons; the earth connection lets them escape to the ground, leaving the sphere positive.
Common mistakeChoosing 'from the earth to the sphere' is what happens with a POSITIVE rod; a negative rod pushes electrons away to earth.
34Short answer · ★ Challenge
Explain why the dome of a machine that builds up very large charges (such as a Van de Graaff generator) is made large, smooth and round.
Show answer
Model answer: A smooth, round surface has no sharp points, so the charge spreads evenly and the charge density stays low everywhere. The field never becomes strong enough to ionise the air, so the charge does not leak away by point action and the dome can hold a large charge.
Common mistakeSaying 'round shapes hold more charge because they are bigger' misses the main reason: there are no points from which charge can leak.
35Multiple choice
In electrostatic spray painting, the paint droplets are charged and the car body is given the opposite charge. One advantage is that:
1. AThe paint dries instantly, because charge produces a lot of heat
2. BThe car body becomes magnetic, so the paint can never flake off
3. CPaint is attracted to hidden parts too, so less is wasted
4. DThe paint changes colour, so it is easy to see where it has gone
Show answer
Answer: C. Paint is attracted to hidden parts too, so less is wasted
Opposite charges attract, so droplets are pulled onto all surfaces, including the back and edges, giving an even coat with little waste.
Common mistakeChoosing 'the paint dries instantly' confuses electrostatic attraction with heating; the charge guides droplets but does not dry them.
36Short answer · ★ Challenge
Describe the electric field pattern between two equal positive charges placed near each other, and explain what is special about the point midway between them.
Show answer
Model answer: Lines leave each charge outwards and curve away from the other charge, so no lines join the two charges. Midway between them the two equal repulsive forces on a test charge are equal and opposite, so the field is zero there: this is a neutral point.
Common mistakeA common error is to draw lines joining the two positive charges; lines only join + to −, so between like charges they bend apart.
37Fill in the blank
The smallest amount of charge that can be carried by a free particle is the charge on one ______, 1.6 × 10⁻¹⁹ C.
Show answer
Answer: electron (or proton)
All charges are whole-number multiples of e = 1.6 × 10⁻¹⁹ C, the size of the charge on an electron or a proton.
Common mistakeWriting 'atom' is wrong because a whole atom is normally neutral.
38Multiple choice
Clothes taken from a tumble dryer often crackle and stick together. Why?
1. ARubbing moves electrons, so the clothes gain opposite charges and attract
2. BThe heat from the dryer makes the cloth magnetic, so the pieces pull together
3. CThe clothes are still damp, and water is sticky, so they cling together
4. DAll the clothes gain the same charge, and like charges attract one another
Show answer
Answer: A. Rubbing moves electrons, so the clothes gain opposite charges and attract
Tumbling rubs different fabrics together; electrons move from one to another, giving opposite charges that attract and small sparks that crackle.
Common mistakeChoosing 'like charges attract' reverses the first law of electrostatics; like charges repel.
39Short answer · ★ Challenge
Two metal spheres A and B on insulating stands touch each other. Describe how a negatively charged rod can be used to give them equal and opposite charges without touching them, and state the charge on each.
Show answer
Model answer: Bring the negative rod near A. Electrons are repelled from A into B. Keeping the rod in place, separate A and B, then remove the rod. A (near the rod) is left positive and B negative, with equal amounts of charge.
Common mistakeRemoving the rod before separating the spheres is the usual error; the electrons then flow back and both spheres are neutral.
40Multiple choice
A charged plastic comb keeps its charge at the end that was rubbed, but a charged metal rod on an insulating handle has charge spread over its whole surface. Why?
1. AElectrons cannot move through plastic, but move freely through metal
2. BPlastic has no electrons at all, but metal has many electrons
3. CMetal stores charge only at its ends, while plastic stores it inside
4. DPlastic attracts charge from the air, and metal pushes it away
Show answer
Answer: A. Electrons cannot move through plastic, but move freely through metal
In insulators electrons are tightly bound, so charge stays where it was placed; in metals free electrons spread charge over the surface.
Common mistakeChoosing 'plastic has no electrons' is wrong: all matter contains electrons; in insulators they are simply not free to move.
41Multiple choice · ★ Challenge
A pair of tiny polystyrene balls hanging on threads are each given 50 nC. When their centres are 5 cm apart, how big is the electric force each exerts on the other? (k = 9 × 10⁹ N m²/C²)
1. A9.0 × 10⁻³ N
2. B9.0 × 10⁻⁷ N
3. C4.5 × 10⁻⁴ N
4. D9.0 × 10³ N
Show answer
Answer: A. 9.0 × 10⁻³ N
F = kq₁q₂/r² = 9 × 10⁹ × (50 × 10⁻⁹)² ÷ (0.05)² = 9 × 10⁹ × 2.5 × 10⁻¹⁵ ÷ 2.5 × 10⁻³ = 9.0 × 10⁻³ N.
Common mistakeChoosing 9.0 × 10⁻⁷ N leaves the distance as 5 (cm) instead of 0.05 m; always change cm to m before squaring.
42Short answer · ★ Challenge
A student wants to test whether the graphite 'lead' of a pencil is a conductor, using a charged gold-leaf electroscope. Describe what she does and what she will observe.
Show answer
Model answer: She holds one end of the pencil lead in her hand (her body connects it to earth) and touches the other end on the cap of the charged electroscope. If graphite is a conductor, the charge flows through it to earth and the leaf falls quickly. If it were an insulator, the leaf would stay open.
Common mistakeLearners forget a path to earth is needed; touching with a conductor that is itself insulated may only share a little charge.
43Fill in the blank
Where electric field lines are drawn closer together, the electric field is ______.
Show answer
Answer: stronger
The density (closeness) of field lines shows the strength of the field.
Common mistakeWriting 'weaker' reverses the meaning of line spacing.
44Short answer
Explain why two bodies rubbed together always end up with equal and opposite charges.
Show answer
Model answer: Rubbing does not create charge; it only moves electrons from one body to the other. The number of electrons lost by one body equals the number gained by the other, so one gets +Q and the other −Q (charge is conserved).
Common mistakeSaying 'rubbing makes charge' is the error; charge is only transferred, never created.
45Multiple choice · ★ Challenge
Charges of +3 μC and −3 μC attract with a force of 0.9 N (k = 9 × 10⁹ N m²/C²). How far apart are they?
1. A0.09 m
2. B0.3 m
3. C3 m
4. D0.03 m
Show answer
Answer: B. 0.3 m
r² = kq₁q₂ ÷ F = 9 × 10⁹ × 3 × 10⁻⁶ × 3 × 10⁻⁶ ÷ 0.9 = 0.09 m², so r = √0.09 = 0.3 m.
Common mistakeChoosing 0.09 m forgets to take the square root: 0.09 is r², not r.
46Short answer
Ball X attracts ball Y. A student says that X and Y must have opposite charges. Is she right? Explain.
Show answer
Model answer: Not necessarily. They may have opposite charges, but one of them could be neutral: a charged ball attracts a neutral one by inducing opposite charge on its near side. Repulsion would be needed to prove both are charged.
Common mistakeAssuming attraction always means opposite charges ignores attraction of neutral objects by induction.
47Short answer · ★ Challenge
A student measures the force between two fixed charges at different separations: r = 0.10 m, F = 3.6 N; r = 0.20 m, F = 0.90 N; r = 0.30 m, F = 0.40 N. Show that the results agree with the inverse square law.
Show answer
Model answer: Calculate F × r² for each: 3.6 × 0.10² = 0.036; 0.90 × 0.20² = 0.036; 0.40 × 0.30² = 0.036 N m². F × r² is constant, so F ∝ 1/r², as Coulomb's law predicts.
Common mistakeA common error is to test F × r (which is not constant: 0.36, 0.18, 0.12) and conclude the law fails; the law involves r².
48Short answer
Workers who handle computer chips in electronics factories wear wrist straps connected to earth. Explain why.
Show answer
Model answer: As they move, their bodies can build up static charge by friction. A sudden discharge (spark) into a chip could damage it. The earthed strap lets charge flow away continuously, so no charge builds up on the worker.
Common mistakeSaying the strap 'protects the worker from shocks' misses the main purpose: protecting delicate chips from static discharge.
49Short answer
A negatively charged rod touches a neutral metal sphere on an insulating stand. Explain, in terms of electrons, what charge the sphere gets.
Show answer
Model answer: Some of the extra electrons on the rod flow onto the sphere when they touch. The sphere now has more electrons than protons, so it becomes negatively charged (the same sign as the rod).
Common mistakeLearners who confuse contact with induction say the sphere becomes positive; by contact the sphere gets the SAME sign as the rod.
50Short answer · ★ Challenge
A balloon gains 2 × 10¹² electrons when rubbed. Calculate its charge and the increase in its mass (electron mass = 9.1 × 10⁻³¹ kg, e = 1.6 × 10⁻¹⁹ C). Comment on the mass change.
Show answer
Model answer: Q = ne = 2 × 10¹² × 1.6 × 10⁻¹⁹ = 3.2 × 10⁻⁷ C (negative). Mass gain = 2 × 10¹² × 9.1 × 10⁻³¹ = 1.82 × 10⁻¹⁸ kg, far too small to measure, so charging does not noticeably change mass.
Common mistakeLearners forget the sign: gaining electrons gives a NEGATIVE charge, −3.2 × 10⁻⁷ C.