AQA A-Level Physics Paper 2, June 2025: Question 12

1 mark · Medium difficulty · Multiple Choice

Determine the electrostatic force between two charged metal spheres with modified charges and radii at a fixed centre-to-centre separation.

Practise this question

Question

Question 12 asks: Two metal spheres each have radius r and charge Q. The force between them is F when the distance between their centres is x. Two other metal spheres each have radius r/2 and charge 2Q. What is the force between these two spheres when the distance between their centres is x? Four multiple choice options are given: A: 4F, B: 2F, C: F, D: F/2.

Mark scheme

Show the mark scheme Mark scheme for question 12 indicates that the correct answer is option A (4F), targeting assessment objective AO2.

How to answer it

Coulomb's Law & Charged Spheres

What this question tests

This question assesses your ability to apply Coulomb's Law to calculate electrostatic forces between charged spherical conductors, and your skill in identifying irrelevant distractor variables.

  • Coulomb's Law: Understanding the proportional relationship between electrostatic force, point charges, and separation: F ∝ (Q₁ × Q₂) / x² .
  • Spherical Symmetry: Recognising that uniformly charged spheres behave electrostatically as if all charge were concentrated at their centres, regardless of their radius (provided they do not touch).
  • Filtering Redundant Information: Identifying that the physical radius of the spheres does not alter the centre-to-centre distance x .
Multiple Choice — Question 12

Electrostatic Force Between Scaled Spheres

AQA A-Level Physics • Paper 2 • Electric Fields

✅ Correct Answer

A: 4F

Award 1 mark [AO2] for selecting option A.

💡 Key Knowledge

  • Coulomb's Law Formula:
    F = (1 / 4πε₀) × (Q₁Q₂ / x²)
  • For spherical conductors, the electric field outside the conductor acts identically to a point charge located at the geometric centre.
  • The radius r only affects surface charge density and potential at the surface—it does not affect the force between centres at a fixed distance x .

📐 Calculations (Step-by-Step)

  1. Initial condition:
    Both spheres have charge Q and separation between centres is x .
    F = k × (Q × Q) / x² = k × Q² / x²
  2. New condition:
    Both spheres now have charge 2Q , and the distance between centres is still x .
    F_new = k × (2Q × 2Q) / x²
  3. Simplifying the expression:
    F_new = k × 4Q² / x² = 4 × [k × Q² / x²] = 4F
  4. Evaluate the effect of radius:
    The radius changed from r to r/2 , but the question explicitly specifies that the centre-to-centre distance remains x . Radius has zero influence on the force.

🧠 Exam Technique

  • Spot the distractor: Examiners often include geometric parameters like sphere radius or mass to see if you can isolate the essential physical quantities. Ask yourself: Does this term appear in the governing formula?
  • Ratio method: When dealing with changes in variables, write down the proportionality:
    F ∝ Q₁ × Q₂
    Since each charge is doubled: 2 × 2 = 4 , so the force must increase by a factor of 4.
  • Speed tip: In section A / multiple choice questions, recognising irrelevant data saves 30–60 seconds of complex arithmetic.

❌ Common Traps & Misconceptions

  • Confusing centre distance with surface gap: Students mistakenly calculate the distance as x − 2r instead of reading carefully that x is already defined as the distance between their centres.
  • Multiplying by 2 instead of 4: Assuming doubling the charge means doubling the force (forgetting that both spheres were given double the charge: 2 × 2 = 4 ). This leads students to incorrectly select B (2F).
  • Trying to factor in capacitance or potential: Remembering V = Q / (4πε₀r) and falsely trying to combine the potential formula with Coulomb's law.

Topics

Physics · 3.7 Fields and their consequences (A-level only)

Question and mark scheme from the AQA A-Level Physics examination, Paper 2, June 2025. QuestionVault is an independent revision resource; questions remain the copyright of the awarding body.