A Level Physics 18.3 Electric Force Between Point Charges MCQs – 30 Practice Questions with Answers (Cambridge 9702)

These 30 original practice MCQs cover Cambridge AS & A Level Physics 9702 Section 18.3, Electric Force Between Point Charges – an A Level (A2) topic. They take you from Coulomb’s law itself, through force calculations (including the electron-proton force inside a hydrogen atom), to combining forces from several charges.

Formula recap: Coulomb’s law: F = Q1Q2 / (4πε0r2), where 1/(4πε0) = 8.99 × 109 m/F (worked as 9.0 × 109 in these questions), ε0 = 8.85 × 10−12 F/m and e = 1.6 × 10−19 C. The force acts along the line joining the charges: like charges repel, unlike charges attract. See the full A Level Physics Formula Sheet for every equation used here.

Coulomb’s Law

Q1. Coulomb’s law states that the force between two point charges is

  • (A) proportional to the sum of the charges and inversely proportional to their separation
  • (B) proportional to the product of the charges and inversely proportional to the square of their separation
  • (C) proportional to the product of the charges and inversely proportional to their separation
  • (D) proportional to the square of the product of the charges and inversely proportional to their separation
Show Answer

Answer: B – F ∝ Q1Q2 / r2. Doubling the separation quarters the force, not halves it, because of the inverse-square dependence.

Q2. Which expression gives the magnitude of the force between point charges Q1 and Q2 separated by distance r in free space?

  • (A) F = Q1Q2 / (4πε0r2)
  • (B) F = Q1Q2 / (4πε0r)
  • (C) F = 4πε0Q1Q2 / r2
  • (D) F = Q1Q2r2 / (4πε0)
Show Answer

Answer: A – F = Q1Q2 / (4πε0r2), with 1/(4πε0) ≈ 8.99 × 109 m/F.

Q3. Two small charged spheres both carry a positive charge. The force between them is

  • (A) attractive, because both charges have the same sign
  • (B) zero, because the forces cancel
  • (C) repulsive, because like charges repel
  • (D) attractive, because positive charges pull together
Show Answer

Answer: C – Like charges (both positive or both negative) repel each other along the line joining them.

Q4. A charge of +3 μC is placed near a charge of −5 μC. The force between them is

  • (A) repulsive, because the charges have different magnitudes
  • (B) zero, because the charges partly cancel
  • (C) repulsive, because one charge is negative
  • (D) attractive, because unlike charges attract
Show Answer

Answer: D – Opposite signs attract, whatever the magnitudes. The magnitudes affect only the size of the force, not its direction.

Q5. Charge Q2 is three times as large as charge Q1. How does the force exerted on Q1 by Q2 compare with the force exerted on Q2 by Q1?

  • (A) The force on Q1 is three times larger
  • (B) The forces are equal in magnitude and opposite in direction
  • (C) The force on Q2 is three times larger
  • (D) The force on Q1 is nine times larger
Show Answer

Answer: B – The two forces form a Newton’s third law pair: equal in magnitude, opposite in direction, even when the charges are very different in size.

Q6. Coulomb’s law in the form F = Q1Q2 / (4πε0r2) treats the charges as point charges. This is a good model when

  • (A) the separation of the charges is much larger than their sizes
  • (B) the charges are stationary in a vacuum only
  • (C) the charges are equal in magnitude
  • (D) the separation of the charges is much smaller than their sizes
Show Answer

Answer: A – When the charges are far apart compared with their own dimensions, each behaves as if all its charge were concentrated at a single point (for a charged sphere, at its centre).

Q7. Newton’s law of gravitation and Coulomb’s law have the same mathematical form. Both forces

  • (A) are always attractive
  • (B) depend on the product of two masses
  • (C) can be either attractive or repulsive
  • (D) follow an inverse-square law with separation
Show Answer

Answer: D – Both F ∝ 1/r2. The differences: gravity depends on masses and is always attractive, while the electric force depends on charges and can attract or repel.

Q8. Which statement correctly compares the electric force between two protons with the gravitational force between them?

  • (A) The two forces are roughly equal in magnitude
  • (B) The gravitational force is much stronger
  • (C) The electric force is enormously stronger, and the protons repel electrically but attract gravitationally
  • (D) The electric force is attractive, like gravity
Show Answer

Answer: C – The Coulomb constant (≈ 9 × 109) is about 1020 times larger than G (6.67 × 10−11), so electric forces between charged particles dwarf their gravitational attraction. Questions 18 and 19 quantify this for a hydrogen atom.

Q9. The value of the constant 1/(4πε0) in Coulomb’s law is approximately

  • (A) 8.99 × 109 m/F
  • (B) 6.67 × 10−11 m/F
  • (C) 8.85 × 10−12 m/F
  • (D) 1.6 × 10−19 m/F
Show Answer

Answer: A – 1/(4πε0) = 8.99 × 109 m/F, where ε0 = 8.85 × 10−12 F/m is the permittivity of free space. Option B is the gravitational constant G.

Q10. Two point charges are held a fixed distance apart. In which direction does the electric force on each charge act?

  • (A) Perpendicular to the line joining the charges
  • (B) In a circle around the other charge
  • (C) At 45° to the line joining the charges
  • (D) Along the line joining the charges
Show Answer

Answer: D – The Coulomb force is a central force: it acts along the line joining the two charges, pulling them together (unlike signs) or pushing them apart (like signs).

Coulomb’s Law Calculations

Q11. Two point charges, each of +1 μC, are separated by 0.30 m in air. The force between them is

  • (A) 0.010 N
  • (B) 0.30 N
  • (C) 0.10 N
  • (D) 1.0 N
Show Answer

Answer: C – F = 9.0 × 109 × (1 × 10−6)2 / (0.30)2 = 9.0 × 10−3 / 0.090 = 0.10 N (repulsive).

Q12. A charge of +2 μC and a charge of −3 μC are 0.10 m apart. The magnitude of the force between them is

  • (A) 0.54 N
  • (B) 5.4 N
  • (C) 54 N
  • (D) 0.054 N
Show Answer

Answer: B – F = 9.0 × 109 × (2 × 10−6)(3 × 10−6) / (0.10)2 = 5.4 × 10−2 / 0.010 = 5.4 N, attractive because the signs are opposite.

Q13. Two point charges a fixed distance apart attract each other with a force of 0.24 N. If the magnitude of one charge is doubled (the other charge and the separation unchanged), the new force is

  • (A) 0.48 N
  • (B) 0.24 N
  • (C) 0.12 N
  • (D) 0.96 N
Show Answer

Answer: A – F ∝ Q1Q2, so doubling one charge doubles the force: 2 × 0.24 = 0.48 N.

Q14. Two point charges repel each other with a force F. Both charges are doubled, with the separation unchanged. The new force is

  • (A) F/4
  • (B) F/2
  • (C) 2F
  • (D) 4F
Show Answer

Answer: D – The product Q1Q2 increases by 2 × 2 = 4, so the force becomes 4F.

Q15. Two point charges attract each other with a force of 0.80 N. Their separation is then doubled, with the charges unchanged. The new force is

  • (A) 0.40 N
  • (B) 0.10 N
  • (C) 1.6 N
  • (D) 0.20 N
Show Answer

Answer: D – F ∝ 1/r2, so doubling r divides the force by 4: 0.80 / 4 = 0.20 N.

Q16. The separation between two point charges is halved. The force between them

  • (A) halves
  • (B) increases by a factor of 4
  • (C) doubles
  • (D) increases by a factor of 21/2
Show Answer

Answer: B – F ∝ 1/r2; replacing r by r/2 multiplies F by 1/(1/2)2 = 4.

Q17. Two point charges of +2 μC each repel each other with a force of 0.40 N. Their separation is

  • (A) 0.30 m
  • (B) 0.090 m
  • (C) 0.030 m
  • (D) 0.90 m
Show Answer

Answer: A – r2 = 9.0 × 109 × (2 × 10−6)2 / 0.40 = 3.6 × 10−2 / 0.40 = 0.090 m2, so r = 0.30 m. (Option B is r2 – remember to take the square root.)

Q18. In a hydrogen atom, an electron (charge −e) is 5.3 × 10−11 m from a proton (charge +e), where e = 1.6 × 10−19 C. The electric force between them is about

  • (A) 8.2 × 10−18 N
  • (B) 4.3 × 10−8 N
  • (C) 8.2 × 10−28 N
  • (D) 8.2 × 10−8 N
Show Answer

Answer: D – F = 9.0 × 109 × (1.6 × 10−19)2 / (5.3 × 10−11)2 = 2.3 × 10−28 / 2.8 × 10−21 = 8.2 × 10−8 N, attractive. It is this force that holds the electron in the atom.

Q19. For the electron and proton in Question 18, the gravitational force between them is about 3.6 × 10−47 N (using G = 6.67 × 10−11 N m2 kg−2, mp = 1.67 × 10−27 kg, me = 9.11 × 10−31 kg). The ratio (electric force) / (gravitational force) is about

  • (A) 2 × 1019
  • (B) 2 × 1029
  • (C) 2 × 1039
  • (D) 2 × 109
Show Answer

Answer: C – Ratio = 8.2 × 10−8 / 3.6 × 10−47 ≈ 2 × 1039. Gravity is utterly negligible inside atoms; the separation cancels in the ratio, so this value is the same at any distance.

Q20. Two identical point charges are 0.10 m apart and repel each other with a force of 0.90 N. Each charge is

  • (A) 10 μC
  • (B) 1 μC
  • (C) 0.1 μC
  • (D) 100 μC
Show Answer

Answer: B – Q2 = F r2 / (9.0 × 109) = 0.90 × 0.010 / 9.0 × 109 = 1.0 × 10−12 C2, so Q = 1.0 × 10−6 C = 1 μC.


Combining Electric Forces

Q21. Charges of +2 μC and +8 μC are fixed 0.30 m apart. A test charge of +1 μC is placed midway between them. The resultant force on the test charge is

  • (A) 3.2 N towards the +8 μC charge
  • (B) 4.0 N towards the +8 μC charge
  • (C) 2.4 N towards the +2 μC charge
  • (D) zero, because it is midway
Show Answer

Answer: C – At 0.15 m from each charge: force from +8 μC = 9.0 × 109 × 8 × 10−12 / 0.0225 = 3.2 N pushing the test charge away from it; force from +2 μC = 0.80 N pushing the opposite way. The forces oppose, so resultant = 3.2 − 0.80 = 2.4 N towards the +2 μC charge.

Q22. A small positive test charge is placed on the line between a +4 μC charge and a +1 μC charge. The point where the resultant force on it is zero lies

  • (A) closer to the +1 μC charge
  • (B) exactly midway between the charges
  • (C) closer to the +4 μC charge
  • (D) outside the two charges, beyond the +4 μC charge
Show Answer

Answer: A – The forces balance where k(4)/x2 = k(1)/(d − x)2. The weaker charge must be nearer for its force to match the stronger charge’s force, so the null point is closer to the smaller charge.

Q23. Charges of +4 μC and +1 μC are fixed 0.30 m apart. The point on the line between them where a test charge experiences no resultant force is

  • (A) 0.10 m from the +4 μC charge
  • (B) 0.15 m from the +4 μC charge
  • (C) 0.24 m from the +4 μC charge
  • (D) 0.20 m from the +4 μC charge
Show Answer

Answer: D – Let x be the distance from the +4 μC charge. Balance: 4/x2 = 1/(0.30 − x)2, so 2/x = 1/(0.30 − x), giving 2(0.30 − x) = x and x = 0.20 m (that is, 0.10 m from the +1 μC charge – closer to the smaller charge, as expected).

Q24. Two charges of +2 μC are fixed 0.20 m apart. A test charge of +1 μC is placed on the same line, 0.10 m beyond the second charge (so it is 0.30 m from the first charge). The resultant force on the test charge is

  • (A) 1.6 N
  • (B) 2.0 N
  • (C) 1.8 N
  • (D) 0.20 N
Show Answer

Answer: B – Both charges repel the test charge in the same direction, so the forces add: from the nearer charge, 9.0 × 109 × 2 × 10−12 / 0.010 = 1.8 N; from the farther charge, 9.0 × 109 × 2 × 10−12 / 0.090 = 0.20 N. Resultant = 1.8 + 0.20 = 2.0 N.

Q25. Charges of +4 μC and −4 μC are fixed 0.20 m apart. A test charge of +1 μC is placed midway between them. The resultant force on the test charge is

  • (A) 7.2 N towards the −4 μC charge
  • (B) zero, because the charges are equal and opposite
  • (C) 3.6 N towards the −4 μC charge
  • (D) 7.2 N towards the +4 μC charge
Show Answer

Answer: A – The +4 μC charge repels the test charge towards the −4 μC charge, and the −4 μC charge attracts it in the same direction. Each force = 9.0 × 109 × 4 × 10−12 / 0.010 = 3.6 N, so the resultant is 3.6 + 3.6 = 7.2 N towards the negative charge.

Q26. Three identical charges of +1 μC are fixed in a straight line, each 0.10 m from the next. The resultant force on the middle charge is

  • (A) 0.90 N
  • (B) 1.8 N
  • (C) zero
  • (D) 0.45 N
Show Answer

Answer: C – Each outer charge repels the middle charge with 0.90 N, but the two forces act in opposite directions and cancel exactly.

Q27. Three identical charges of +1 μC are fixed in a straight line with 0.30 m between neighbouring charges. The resultant force on one of the end charges is

  • (A) 0.10 N
  • (B) 0.20 N
  • (C) 0.15 N
  • (D) 0.125 N
Show Answer

Answer: D – Both other charges repel the end charge in the same direction. From the middle charge (0.30 m): 9.0 × 109 × 1 × 10−12 / 0.090 = 0.10 N. From the far charge (0.60 m): 9.0 × 10−3 / 0.36 = 0.025 N. Resultant = 0.10 + 0.025 = 0.125 N.

Q28. Three charges of +1 μC are fixed at the corners of an equilateral triangle of side 0.30 m. The magnitude of the resultant force on one of the charges is about

  • (A) 0.10 N
  • (B) 0.17 N
  • (C) 0.20 N
  • (D) 0.30 N
Show Answer

Answer: B – Each of the other charges repels it with F = 9.0 × 109 × 1 × 10−12 / 0.090 = 0.10 N, and the two forces act at 60° to each other. By symmetry the resultant lies along the bisector: R = 2F cos 30° = 2 × 0.10 × 0.866 = 0.17 N, directed away from the triangle.

Q29. Charges of +9 μC and −1 μC are fixed some distance apart. On the line through the charges, a test charge can experience zero resultant force

  • (A) only outside the charges, on the side of the −1 μC charge
  • (B) only between the two charges
  • (C) only outside the charges, on the side of the +9 μC charge
  • (D) at no point, because the charges have opposite signs
Show Answer

Answer: A – Between opposite charges both forces on a test charge act in the same direction, so they can never cancel there. Outside, the forces oppose; cancellation is possible only on the side of the smaller-magnitude charge, where the test charge can be near the weak charge and far from the strong one.

Q30. Charges of +8 μC and +2 μC are fixed 0.40 m apart. A test charge of +1 μC is placed on the line between them, 0.10 m from the +8 μC charge. The resultant force on the test charge is

  • (A) 7.4 N towards the +8 μC charge
  • (B) 7.2 N towards the +2 μC charge
  • (C) 7.0 N towards the +2 μC charge
  • (D) 7.0 N towards the +8 μC charge
Show Answer

Answer: C – Force from +8 μC (0.10 m away): 9.0 × 109 × 8 × 10−12 / 0.010 = 7.2 N, pushing the test charge towards the +2 μC charge. Force from +2 μC (0.30 m away): 9.0 × 109 × 2 × 10−12 / 0.090 = 0.20 N, pushing it back. Resultant = 7.2 − 0.20 = 7.0 N towards the +2 μC charge.

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These are original practice questions written for revision, in the style of Cambridge AS & A Level Physics 9702. They are not Cambridge past-paper questions, and this page is not affiliated with Cambridge Assessment International Education.