Senior 2 practice book · Unit 9 of 10

Electric Field and Applications of Electrostatics

50 questions that complete the Senior 2 quiz for this unit: 25 core and 25 challenge. Easy and hard questions are mixed. Try each question, then tap “Show answer”.

Common misconceptions

If a bigger charge is placed at a point, the electric field strength there becomes bigger.The field at a point is set by the charges that CREATE it. A bigger test charge feels a bigger force, but E = F/q stays the same.
Field lines show the actual path a charged particle always follows.A field line shows the direction of the force on a positive charge at each point. A moving particle that already has a velocity can cross field lines.
Rubber tyres protect people in a car from lightning.A few centimetres of rubber cannot stop a lightning flash that has crossed kilometres of air. The metal body of the car acts as a Faraday cage: the charge flows round the outside to earth.
The field between charged parallel plates is strongest near the plates.Between large parallel plates the field is uniform: it has the same strength and direction everywhere except near the edges.
Static electricity is only a harmless nuisance.Sparks from built-up static charge can ignite fuel vapour, flour dust or gas, and can damage electronic chips; earthing is needed to prevent this.

What this unit covers

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

Electric field and electric field-line patterns
Electric field strength E = F/q
Coulomb's law F = kq₁q₂/r²
Field of a point charge E = kQ/r²
Uniform field between parallel plates E = V/d
Superposition of electric forces and fields
Electric potential, potential difference and work W = qV
Acceleration and kinetic energy of charged particles in an electric field
Charge on conductors: sharp points, hollow conductors and lightning conductors
Van de Graaff generator
Electrostatic precipitators and electrostatic paint spraying
Photocopiers, printers and electrostatic crop spraying
Dangers of static electricity and earthing
Electric shielding: the Faraday cage

Go to the questions

Questions (1–50)

Easier and harder questions are mixed, just like in a real exam. The 25 harder ones are marked ★ Challenge.

1True or false
In an electrostatic precipitator, the collecting plates are given the same charge as the dust particles.
Show answer
Answer: False
The plates carry the opposite charge (or are earthed), so that the charged dust is attracted to them.
Common mistakeLike charges repel; plates with the same charge would push the dust away, back into the chimney.
2True or false · ★ Challenge
Bringing a strongly charged rod near a closed metal box produces an electric field inside the box.
Show answer
Answer: False
Charges in the metal rearrange so that the field inside the closed conductor is zero; the box shields its inside.
Common mistakeLearners expect fields to pass through everything; a closed conductor keeps electric fields out.
3True or false
If charge A is much bigger than charge B, the electric force on A due to B is smaller than the force on B due to A.
Show answer
Answer: False
The two forces are a Newton's third law pair: equal in size and opposite in direction, whatever the sizes of the charges.
Common mistakeLearners expect the bigger charge to 'win'; both feel the same size of force, F = kq₁q₂/r².
4True or false · ★ Challenge
A positive charge released from rest in an electric field moves from a point of higher potential towards a point of lower potential.
Show answer
Answer: True
The force on a positive charge points along the field, which points from high potential to low potential.
Common mistakeSome think all charges move to higher potential; only NEGATIVE charges (such as electrons) do.
5True or false
A charge put on an isolated metal sphere spreads out evenly over its outer surface, because a sphere has no sharp points.
Show answer
Answer: True
All parts of a sphere's surface are equally curved, so the charge density is the same everywhere on it.
Common mistakeSome think charge collects at the 'bottom' of a sphere; it spreads evenly over the outer surface.
6True or false · ★ Challenge
Between two large charged parallel plates, a small charge feels a larger force near the positive plate than in the middle.
Show answer
Answer: False
The field between the plates is uniform, so F = qE is the same everywhere between them (except near the edges).
Common mistakeLearners picture the field like that of a point charge, strongest near the charge; parallel plates give a uniform field.
7True or false
At any point, an electric field line shows the direction in which a small positive charge placed there would start to move.
Show answer
Answer: True
The direction of the field is the direction of the force on a positive test charge; released from rest it starts to move along the line.
Common mistakeSome think field lines show the direction a negative charge moves; a negative charge moves opposite to the lines.
8Multiple choice · ★ Challenge
How does an electrostatic (continuous-jet) inkjet printer steer its ink drops onto the right place?
1. AIt blows the drops sideways with a fan
2. BIt fires each drop from a different nozzle
3. CIt uses magnets to pull the drops
4. DIt charges the drops and deflects them between plates
Show answer
Answer: D. It charges the drops and deflects them between plates
Each drop is given a charge and passes between deflecting plates; changing the plate voltage changes the force and so where the drop lands.
Common mistake'Magnets' is tempting, but ink drops are steered by ELECTRIC forces on their charge.
9True or false
In electrostatic crop spraying, the charged droplets spread out because they repel each other, and they are attracted to the plants, even to the undersides of leaves.
Show answer
Answer: True
Like-charged drops repel, giving an even spray, and the earthed plants attract them, so less spray is wasted.
Common mistakeSome think charging is only to make drops smaller; its main purpose is attraction to the plants.
10Multiple choice · ★ Challenge
A pear-shaped metal conductor is charged. Where is the electric field just outside its surface strongest?
1. AInside the conductor
2. BEqually strong all over the surface
3. CAt the wide, gently curved end
4. DAt the narrow, sharply curved end
Show answer
Answer: D. At the narrow, sharply curved end
Charge gathers most densely where the surface is most sharply curved, so the field is strongest at the narrow end.
Common mistake'Equally strong' is true only for a sphere; on other shapes charge collects at the sharpest parts.
11Fill in the blank
The drum of a photocopier is coated with a material that loses its charge where ______ falls on it.
Show answer
Answer: light
The coating conducts when light falls on it, so charge leaks away from the lit areas.
Common mistakeWriting 'toner' confuses the order of steps; the toner arrives AFTER the light has made the charged image.
12Multiple choice · ★ Challenge
In electrostatic paint spraying of a bicycle frame, paint also coats the back of the frame, facing away from the spray gun. Why?
1. AThe charged drops follow field lines round to the back
2. BGravity pulls the drops round the frame
3. CThe drops are uncharged, so they spread out evenly everywhere
4. DThe paint bounces off the walls of the room
Show answer
Answer: A. The charged drops follow field lines round to the back
The earthed (or oppositely charged) frame attracts the charged droplets; the field lines curve round the frame, so drops reach hidden surfaces too.
Common mistake'The drops are uncharged' is wrong: the method works BECAUSE the drops are charged and attracted to the frame.
13Fill in the blank
A closed metal container that keeps external electric fields out of the space inside it is called a ______ cage.
Show answer
Answer: Faraday
Named after Michael Faraday, who showed that the field inside a closed conductor is zero.
Common mistakeWriting 'Van de Graaff' confuses a shield with a machine that produces high voltage.
14Multiple choice · ★ Challenge
A small metal ball hanging on a nylon thread touches the charged dome of a Van de Graaff generator and is then pushed away from it. Why?
1. AIt gains charge of the same sign, and like charges repel
2. BIt loses all its electrons
3. CIt gains the opposite charge, so it is attracted
4. DThe nylon thread becomes charged and repels the whole dome
Show answer
Answer: A. It gains charge of the same sign, and like charges repel
On contact, some of the dome's charge flows onto the ball; ball and dome then carry like charges and repel.
Common mistake'It gains the opposite charge' describes charging by induction before contact, not after touching.
15True or false
An uncharged particle placed in a uniform electric field between charged plates feels no resultant electric force.
Show answer
Answer: True
F = qE; with q = 0 there is no resultant electric force (only its weight acts).
Common mistakeSome think every particle between charged plates is pulled to a plate; only charged particles are.
16Fill in the blank · ★ Challenge
Inside a smoke detector, an alpha particle carrying 3.2 × 10⁻¹⁹ C crosses a 2000 V gap, starting from rest. Its gain in kinetic energy is ______ J.
Show answer
Answer: 6.4 × 10⁻¹⁶
KE gained = qV = 3.2 × 10⁻¹⁹ × 2000 = 6.4 × 10⁻¹⁶ J.
Common mistakeUsing the electron charge (1.6 × 10⁻¹⁹ C) halves the answer; an alpha particle carries two units of charge.
17True or false
If two charges each produce a field of 500 N/C at a point, the total field there must be 1000 N/C.
Show answer
Answer: False
Fields add as vectors; the total can be anything from 0 N/C (opposite directions) to 1000 N/C (same direction).
Common mistakeAdding the sizes without looking at the directions is the error; direction always matters for fields.
18Short answer · ★ Challenge
What is a Faraday cage? Explain how it works and give one use.
Show answer
Model answer: A Faraday cage is a closed box or mesh made of a conductor such as metal. Charges in the conductor move so that the field inside cancels; any charge stays on the outer surface, so there is no electric field inside. Uses: protecting sensitive equipment from electric fields, shielding cables, cars and aircraft protecting passengers from lightning, the metal walls of a microwave oven.
Common mistakeSome think the cage must be solid metal; a fine metal mesh works just as well.
19Multiple choice
In a Van de Graaff generator, how is charge carried up to the metal dome?
1. AAlong the metal support column
2. BThrough wires inside the column
3. COn a moving insulating belt
4. DBy the air around the dome
Show answer
Answer: C. On a moving insulating belt
Charge is sprayed onto a moving rubber belt, which carries it up to the dome, where a metal comb collects it.
Common mistake'Along the metal column' would let the charge leak away; the column is an insulator.
20Short answer · ★ Challenge
Describe the main steps by which a photocopier makes a copy of a page.
Show answer
Model answer: (1) The drum is given an electric charge. (2) Light reflected from the page falls on the drum: white parts send light, which discharges the drum there; dark parts send no light, leaving a charged image. (3) Toner of opposite charge is attracted to the charged parts. (4) Charged paper attracts the toner off the drum. (5) The paper is heated, so the toner melts and sticks permanently.
Common mistakeLeaving out the role of light is common; light is what removes charge from the parts that must stay white.
21Multiple choice
A proton is released from rest in a uniform electric field. How does it move?
1. AIt moves in a circle around the field lines
2. BIt speeds up steadily along the field
3. CIt speeds up steadily against the field
4. DIt moves at a constant speed along the field
Show answer
Answer: B. It speeds up steadily along the field
The force qE is constant and along the field (the proton is positive), so it has a constant acceleration in the field direction.
Common mistake'Constant speed' forgets that a constant resultant force produces a constant ACCELERATION.
22Multiple choice · ★ Challenge
An electron (charge −1.6 × 10⁻¹⁹ C) is in a uniform field of 1000 N/C pointing east. What force acts on it?
1. A6.3 × 10²¹ N towards the west
2. B1.6 × 10⁻¹⁶ N towards the east
3. C1.6 × 10⁻¹⁶ N towards the west
4. D1.6 × 10⁻²² N towards the west
Show answer
Answer: C. 1.6 × 10⁻¹⁶ N towards the west
F = qE = 1.6 × 10⁻¹⁹ × 1000 = 1.6 × 10⁻¹⁶ N; the electron is negative, so the force is opposite to the field: west.
Common mistake'Towards the east' forgets that the force on a NEGATIVE charge is opposite to the field direction.
23Fill in the blank
The electric field strength of a point charge is inversely proportional to the ______ of the distance from the charge.
Show answer
Answer: square
E = kQ/r², so E ∝ 1/r².
Common mistakeWriting 'distance' alone (E ∝ 1/r) is the usual slip; the dependence is on r squared.
24Multiple choice · ★ Challenge
In a laboratory, two charged spheres act at a test point P: one sphere's field there is 4000 N/C due east, the other's is 3000 N/C due north. How strong is the combined field at P?
1. A5000 N/C
2. B3500 N/C
3. C7000 N/C
4. D1000 N/C
Show answer
Answer: A. 5000 N/C
The fields are at right angles, so they add as vectors: E = √(4000² + 3000²) = √(25 × 10⁶) = 5000 N/C.
Common mistake7000 N/C simply adds the numbers, which is only right when both fields point the same way.
25Fill in the blank
The volt, the unit of potential difference, is equal to one ______ per coulomb.
Show answer
Answer: joule
V = W/q, so 1 V = 1 J/C.
Common mistakeWriting 'newton per coulomb' gives the unit of field strength, not of potential difference.
26Short answer · ★ Challenge
Explain why the dome of a Van de Graaff generator is made large and smooth (rounded) rather than small or pointed.
Show answer
Model answer: On a large, smooth dome the charge spreads out thinly with no sharp points, so the field at the surface stays below the value at which air breaks down. Charge does not leak away into the air, so a very large charge, and a very high voltage, can build up.
Common mistakeSome think the shape is just for safety; the key point is that sharp or small surfaces leak charge.
27Fill in the blank
If the charge placed at a point in an electric field is doubled, the force on it doubles but the electric field strength at that point ______.
Show answer
Answer: stays the same (is unchanged)
E = F/q: F and q both double, so their ratio, the field strength, is unchanged.
Common mistakeLearners think a bigger test charge makes a stronger field; the field is created by OTHER charges.
28Short answer · ★ Challenge
In the dry season, a learner walking across a nylon carpet feels a small electric shock when he touches a metal door handle. Explain why.
Show answer
Model answer: Friction between his shoes and the carpet transfers electrons, so his body becomes charged; his rubber soles insulate him from the ground, so the charge builds up. When his hand comes near the metal handle (which is connected to earth), the charge jumps across as a spark and flows to earth, which he feels as a shock. Dry air conducts poorly, so more charge builds up in the dry season.
Common mistakeSaying the shock comes from the handle is the usual error; the charge was on his body.
29Multiple choice
The distance between two small charged spheres is halved, with their charges unchanged. The force between them becomes:
1. AA quarter as large
2. BHalf as large
3. C2 times as large
4. D4 times as large
Show answer
Answer: D. 4 times as large
F ∝ 1/r²: halving r makes F (1/0.5)² = 4 times as large.
Common mistake'2 times' forgets the square in Coulomb's law; 'a quarter' gets the inverse-square rule the wrong way round.
30Short answer · ★ Challenge
A negatively charged oil drop moves horizontally into the space between two horizontal plates; the top plate is positive. Describe its path between the plates, and say how the path changes if the voltage is increased.
Show answer
Model answer: The electric force on the negative drop is upwards, towards the positive plate, and stays constant. If it is larger than the drop's weight, the drop keeps its horizontal speed but accelerates upwards, so its path curves upwards (a parabola). Increasing the voltage increases E = V/d and the upward force, so the drop curves upwards more sharply.
Common mistakeMany say the drop moves straight to the top plate; it keeps its horizontal velocity, so the path is a curve.
31Multiple choice
At what distance from a point charge is the field strength one quarter of its value at 5 cm?
1. A2.5 cm
2. B10 cm
3. C1.25 cm
4. D20 cm
Show answer
Answer: B. 10 cm
E ∝ 1/r²: for E to become 1/4, r² must be 4 times as large, so r doubles: 2 × 5 = 10 cm.
Common mistake20 cm assumes E ∝ 1/r (four times the distance); because of the square, doubling r is enough.
32Multiple choice · ★ Challenge
What is the acceleration of an electron (mass 9.1 × 10⁻³¹ kg, charge 1.6 × 10⁻¹⁹ C) in a uniform field of 910 N/C?
1. A1.6 × 10¹⁴ m/s²
2. B1.6 × 10¹¹ m/s²
3. C1.5 × 10⁻¹⁶ m/s²
4. D1.3 × 10⁻⁴⁶ m/s²
Show answer
Answer: A. 1.6 × 10¹⁴ m/s²
F = qE = 1.6 × 10⁻¹⁹ × 910 ≈ 1.46 × 10⁻¹⁶ N; a = F/m = 1.46 × 10⁻¹⁶ ÷ 9.1 × 10⁻³¹ = 1.6 × 10¹⁴ m/s².
Common mistake1.5 × 10⁻¹⁶ is the FORCE in newtons, not the acceleration; you must still divide by the mass.
33Multiple choice · ★ Challenge
The field 0.50 m from the centre of a charged Van de Graaff dome is 1.8 × 10⁵ N/C. Treating the dome as a point charge at its centre, what is its charge? (k = 9 × 10⁹ N m²/C²)
1. A5 μC
2. B10 μC
3. C0.5 μC
4. D2.5 μC
Show answer
Answer: A. 5 μC
Q = Er²/k = 1.8 × 10⁵ × 0.50² ÷ (9 × 10⁹) = 4.5 × 10⁴ ÷ 9 × 10⁹ = 5 × 10⁻⁶ C = 5 μC.
Common mistake10 μC comes from using r instead of r²; the field of a point charge falls off with the square of the distance.
34Multiple choice
A potential difference of 1 V between two points means that:
1. A1 C of charge flows each second
2. B1 J of work is done each second the charge flows
3. C1 J of work is done per coulomb moved
4. D1 N of force acts on each coulomb
Show answer
Answer: C. 1 J of work is done per coulomb moved
V = W/q, so 1 V = 1 J/C: one joule of work for each coulomb moved between the points.
Common mistake'1 J each second' describes a power of 1 W, not a potential difference.
35Multiple choice
Why is a person inside a car usually safe if the car is struck by lightning?
1. AThe car's battery cancels the charge
2. BCharge flows round the metal body to earth
3. CThe glass windows absorb the charge
4. DThe rubber tyres stop the current reaching the ground
Show answer
Answer: B. Charge flows round the metal body to earth
The metal body acts as a Faraday cage: the charge stays on the outside surface and passes to the ground, leaving no field inside.
Common mistake'The rubber tyres' is the popular myth; a flash that has crossed kilometres of air easily crosses a few centimetres of rubber.
36Short answer · ★ Challenge
A student draws the field of an isolated negative charge and writes: 'The lines start on the negative charge, some lines cross near the charge, and the lines are evenly spaced everywhere.' Identify and correct the three errors.
Show answer
Model answer: (1) The lines should END on the negative charge, pointing radially inwards, because field lines go towards negative charges. (2) Field lines never cross, since the field has only one direction at each point. (3) The lines are closest together near the charge, where the field is strongest, and spread out further away.
Common mistakeThe commonest error is drawing arrows outwards from a negative charge; arrows always point towards negative charges.
37Multiple choice
Why is it dangerous to shelter under a tall, lonely tree during a thunderstorm?
1. ATrees attract lightning because they are full of iron
2. BThe leaves collect static charge from the rain
3. CThe tree blocks the lightning conductor's protection
4. DThe tree may be struck and current can jump to you
Show answer
Answer: D. The tree may be struck and current can jump to you
Tall isolated objects are the most likely to be struck; the current can then jump from the trunk to a person standing close by (side flash).
Common mistake'Full of iron' is a myth; the tree is struck because it is tall and damp enough to conduct.
38Multiple choice · ★ Challenge
In a thunderstorm the potential difference between a cloud and the ground is 1 × 10⁸ V. A lightning flash carries 20 C. How much energy is transferred?
1. A5 × 10⁶ J
2. B2 × 10⁷ J
3. C2 × 10⁹ J
4. D2 × 10⁻⁷ J
Show answer
Answer: C. 2 × 10⁹ J
W = qV = 20 × 1 × 10⁸ = 2 × 10⁹ J.
Common mistake5 × 10⁶ J divides V by q; energy is charge MULTIPLIED by potential difference.
39Multiple choice
Two equal positive charges are placed near each other. Which describes their field lines?
1. ALines come in from far away and go into both of the charges
2. BLines curve away from each other, leaving a field-free point midway
3. CLines go straight from one charge to the other
4. DLines form closed circles round each charge
Show answer
Answer: B. Lines curve away from each other, leaving a field-free point midway
Like charges repel: their lines bend away from each other and there is a neutral point halfway between them.
Common mistake'Lines go from one charge to the other' describes a positive and a NEGATIVE charge, not two positives.
40Multiple choice · ★ Challenge
Two identical small conducting spheres carry +6 μC and −2 μC. They are touched together and then put back at the same distance apart. Compared with before, the force between them is:
1. AZero, because the charges cancel
2. BThe same size, and now repulsive
3. CThree times as big, and still attractive
4. DOne third as big, and now repulsive
Show answer
Answer: D. One third as big, and now repulsive
Sharing gives each (+6 − 2) ÷ 2 = +2 μC. F ∝ q₁q₂: before 6 × 2 = 12, after 2 × 2 = 4, so the force is 1/3 as big; both are now positive, so they repel.
Common mistake'Zero' assumes the charges cancel completely; they only partly cancel, leaving +4 μC to share.
41Multiple choice
Why does a technician repairing a computer wear an anti-static wrist strap connected to earth?
1. ASo charge on her body flows away before sparks harm chips
2. BTo make her hands stick firmly to the circuit board she repairs
3. CTo keep the computer's battery charged
4. DTo protect her from a mains electric shock
Show answer
Answer: A. So charge on her body flows away before sparks harm chips
The strap lets charge on her body flow safely to earth, so no spark jumps to sensitive chips and damages them.
Common mistake'To protect her from mains shock' is wrong: earthing her body would make a mains shock MORE dangerous, which is why the strap has a high resistance.
42Short answer · ★ Challenge
A school in Nyamagabe fixes a pointed copper lightning conductor to its roof, but joins the bottom of the copper strip to a dry wooden post instead of to a metal plate buried in damp soil. Evaluate this installation.
Show answer
Model answer: It will not protect the building. Dry wood is an insulator, so charge collected at the points cannot flow to earth; charge builds up on the conductor, and a strike would not be carried safely to the ground but could jump (spark) to the building, causing fire or injury. The strip must end in a metal plate buried in damp earth.
Common mistakeThinking the sharp points alone give protection is the usual mistake; there must be a low-resistance path to earth.
43Multiple choice
In a photocopier, why does the toner powder stick to the drum only where the dark parts of the image are?
1. AThose parts are hotter than the rest
2. BThe drum is uncharged everywhere the image is dark
3. CThose parts stay charged; light discharged the rest
4. DToner is magnetic and sticks to the ink
Show answer
Answer: C. Those parts stay charged; light discharged the rest
The charged drum loses its charge where light from white areas falls on it; dark areas reflect no light, so they stay charged and attract the toner.
Common mistake'The drum is uncharged where the image is dark' reverses the process: light removes the charge, so the WHITE areas are uncharged.
44Multiple choice · ★ Challenge
In a particle accelerator, a proton (mass 1.67 × 10⁻²⁷ kg, charge 1.6 × 10⁻¹⁹ C) starts at rest and is pushed across a 1000 V gap. How fast is it then moving?
1. A3.1 × 10⁵ m/s
2. B4.4 × 10⁵ m/s
3. C1.9 × 10¹¹ m/s
4. D1.4 × 10⁴ m/s
Show answer
Answer: B. 4.4 × 10⁵ m/s
KE = qV = 1.6 × 10⁻¹⁹ × 1000 = 1.6 × 10⁻¹⁶ J; v = √(2KE/m) = √(2 × 1.6 × 10⁻¹⁶ ÷ 1.67 × 10⁻²⁷) ≈ 4.4 × 10⁵ m/s.
Common mistake1.9 × 10¹¹ m/s forgets the square root (that is v², faster than light!); 3.1 × 10⁵ m/s forgets the 2 in ½mv².
45Multiple choice
The field between two parallel plates 4 cm apart is 5000 V/m. What is the potential difference between the plates?
1. A20 000 V
2. B200 V
3. C125 000 V
4. D1250 V
Show answer
Answer: B. 200 V
V = Ed = 5000 × 0.04 = 200 V.
Common mistake20 000 V uses d = 4 instead of 0.04 m; 1250 V divides E by d (in cm) instead of multiplying.
46Short answer · ★ Challenge
Charges of +4 μC and +2 μC are 0.20 m apart. A +1 nC test charge is placed exactly halfway between them. Find the resultant force on the test charge and its direction (k = 9 × 10⁹ N m²/C²).
Show answer
Model answer: Each charge is 0.10 m away. From +4 μC: F = 9 × 10⁹ × 4 × 10⁻⁶ × 1 × 10⁻⁹ ÷ 0.10² = 3.6 × 10⁻³ N, pushing towards the +2 μC charge. From +2 μC: 1.8 × 10⁻³ N, pushing towards the +4 μC charge. Resultant = 3.6 × 10⁻³ − 1.8 × 10⁻³ = 1.8 × 10⁻³ N towards the +2 μC charge.
Common mistakeAdding the two forces (5.4 × 10⁻³ N) ignores that both charges repel the test charge in OPPOSITE directions.
47Multiple choice
A tiny dust particle carrying 5 nC is in the Earth's fair-weather electric field of 100 N/C. What force acts on it?
1. A5 × 10⁻⁴ N
2. B2 × 10¹⁰ N
3. C5 × 10⁻⁷ N
4. D500 N
Show answer
Answer: C. 5 × 10⁻⁷ N
F = qE = 5 × 10⁻⁹ × 100 = 5 × 10⁻⁷ N.
Common mistake5 × 10⁻⁴ N treats nC as μC (10⁻⁶); 2 × 10¹⁰ N divides E by q instead of multiplying.
48Short answer · ★ Challenge
A +4 μC charge feels a repulsive force of 1.6 N from a small charged sphere 0.15 m away. Find the charge on the sphere (k = 9 × 10⁹ N m²/C²).
Show answer
Model answer: F = kq₁q₂/r², so q₂ = Fr² ÷ (kq₁) = 1.6 × 0.15² ÷ (9 × 10⁹ × 4 × 10⁻⁶) = 0.036 ÷ 36 000 = 1 × 10⁻⁶ C = +1 μC (positive, since the force is repulsive).
Common mistakeForgetting to square 0.15 m gives a charge 1/0.15 ≈ 7 times too large.
49Short answer
Why must the collecting plates of an electrostatic precipitator be shaken or knocked regularly?
Show answer
Model answer: Dust and soot build up on the plates. Knocking them makes the dust fall into a collecting hopper below. Otherwise the thick layer would reduce the attraction and stop the precipitator working well, and dust could be blown back into the chimney.
Common mistakeSome think the plates keep working forever; collected dust must be removed for the plates to go on attracting.
50Short answer · ★ Challenge
A small sphere with a fixed charge hangs between two parallel plates with 2000 V across them. The plate separation d is changed: d = 2 cm, F = 4 mN; d = 4 cm, F = 2 mN; d = 8 cm, F = 1 mN. State the relationship between F and d, and find the charge on the sphere.
Show answer
Model answer: When d doubles, F halves, so F is inversely proportional to d (F × d is constant). F = qE = qV/d, so q = Fd/V = 0.004 × 0.02 ÷ 2000 = 4 × 10⁻⁸ C.
Common mistakeForgetting to change mN to N and cm to m gives an answer 10⁵ times too large.