Grade 11 Physical Sciences · Electricity and Magnetism

Apply Coulomb's law

Calculate the force between two charges using F = kQ₁Q₂/r², and say how the force changes when the distance changes.

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Electrostatics grade 11: IntroductionKevinmathscience

Coulomb's Law Electrostatics grade 11 and 12Miss Martins Maths and Science

Physics 12.2.1b - Coulomb`s Law - Simple ExamplesDerek Owens

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Question 7.5 · November 2025 · Paper 1 · National (DBE) · 2 marks

A sphere X is placed at point A on a horizontal surface. X carries a charge of

+ 3 \times 1 0^{- 7}

C. Point P is r metres to the left of point A, as shown in the diagram below.

The magnitude of the electric field at point P is

1, 08 \times 1 0^{6}

N·C

^{- 1}

7.5 Sphere Y is brought into contact with sphere X, and is placed back in its original position.

How will the magnitude of the force that sphere X now exerts on sphere Y be affected? Choose from INCREASES, DECREASES or REMAINS THE SAME.(2)

Work it out on paper first. Then mark yourself with the official memo, one tick at a time.

More past paper questions: apply coulomb's law

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3. Question 7.3 · May/June 2023 · Paper 1 · National (DBE) · 3 marks
Two point charges, X and Y, are held $0, 03$ m apart, as shown in the diagram below. The charge of X is $- 7, 2 \times 1 0^{- 9}$ C, while the charge of Y is $+ 7, 2 \times 1 0^{- 9}$ C.
7.3 Calculate the magnitude of the electrostatic force that Y exerts on X.(3)
Show the memo (3 ticks)Memo
1. ✓
  Formula $F = \frac{k Q _{Y} Q _{X}}{r ^{2}}$
  1 mark · Apply Coulomb's law
2. ✓
  Substitution $F = \frac{( 9 \times 1 0 ^{9} ) ( 7 , 2 \times 1 0 ^{- 9} ) ( 7 , 2 \times 1 0 ^{- 9} )}{( 0 , 03 ) ^{2}}$
  1 mark · Apply Coulomb's law
3. ✓
  Answer with unit $F = 5, 18 \times 1 0^{- 4}$ N ( $0, 000518$ N)
  1 mark · Apply Coulomb's law
4. Question 1.7 · November 2022 · Paper 1 · National (DBE) · 2 marks
Various options are provided as possible answers to the following questions. Each question has only ONE correct answer.
1.7 A proton and an electron are a distance $r$ apart. The magnitude of the electrostatic force that they exert on each other is $F$ .

Which ONE of the following graphs shows the relationship between $F$ and $r^{2}$ as the proton and the electron approach each other?(2)
1. A
2. B
3. C
4. D
Show the memo (1 tick)Memo
1. ✓
  Inverse-square relationship $F = \frac{k Q _{1} Q _{2}}{r ^{2}}$ , so $F \propto \frac{1}{r ^{2}}$ : $F$ is inversely proportional to $r^{2}$ .
  A graph of $F$ against $r^{2}$ is therefore a hyperbola that gets very large as $r^{2}$ becomes small and approaches zero as $r^{2}$ becomes large (graph C).
  
  Answer: C
  2 marks · Apply Coulomb's law
5. Question 1.7 · May/June 2022 · Paper 1 · National (DBE) · 2 marks
Various options are provided as possible answers to the following questions. Each question has only ONE correct answer. Choose the answer and write only the letter (A–D) next to the question numbers (1.1 to 1.10) in the ANSWER BOOK, e.g. 1.11 E.
1.7 Two oppositely charged point charges move towards each other.

Which ONE of the following is CORRECT?

The point charges move at ...(2)
1. A constant velocity.
2. B decreasing velocity.
3. C constant acceleration.
4. D increasing acceleration.
Show the memo (1 tick)Memo
1. ✓
  Choose the correct optionOpposite charges attract, so they speed up towards each other. As $r$ decreases, $F = \frac{k Q _{1} Q _{2}}{r ^{2}}$ increases, so the acceleration $a = \frac{F}{m}$ increases.
  
  Answer: D
  2 marks · Apply Coulomb's law
6. Question 7.4 · November 2022 · Paper 1 · National (DBE) · 5 marks
A charged sphere M is suspended from a ceiling by a light inextensible, insulated string.

Another charged sphere N, of mass $2, 04 \times 1 0^{- 3}$ kg and carrying a charge of $+ 8, 6 \times 1 0^{- 8}$ C, hangs STATIONARY vertically below sphere M. The centres of the spheres are $0, 3$ m apart, as shown in the diagram below.
7.4 Calculate the magnitude of the charge on sphere M.(5)
Show the memo (5 ticks)Memo
1. ✓
  Weight of N $F_{g} = m g = (2, 04 \times 1 0^{- 3}) (9, 8) = 0, 02$ N
  1 mark · Calculate weight
2. ✓
  Coulomb's formula $F = \frac{k Q _{M} Q _{N}}{r ^{2}}$
  1 mark · Apply Coulomb's law
3. ✓
  Equating forces ( $F_{n e t} = 0$ ) $F_{n e t} = m g - \frac{k Q _{M} Q _{N}}{r ^{2}}$
  $0 = 0, 02 - \frac{k Q _{M} Q _{N}}{r ^{2}}$ (OR $m g = \frac{k Q _{M} Q _{N}}{r ^{2}}$ )
  1 mark · Apply Newton's second law
4. ✓
  Substitution into Coulomb's law $\frac{( 9 \times 1 0 ^{9} ) Q _{M} ( 8 , 6 \times 1 0 ^{- 8} )}{( 0 , 3 ) ^{2}}$
  1 mark · Apply Coulomb's law
5. ✓
  Answer $Q_{M} = 2, 33 \times 1 0^{- 6}$ C
  1 mark · Apply Coulomb's law

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