Electric potentialAQA A-Level Physics: Subtopic test

1. 1
   A small sphere carries a charge of +6.0 nC, which may be treated as a point charge at its centre. The sphere is isolated in a vacuum (ε₀ = 8.85 × 10⁻¹² F m⁻¹).

   (a)

   What is the electric potential at a point 0.30 m from the centre of the sphere?

   [1 mark]

   • A1.8 × 10² V
   • B6.0 × 10² V
   • C1.6 × 10¹ V
   • D2.2 × 10⁻¹⁸ V

   (b)

   What is the work done in bringing a small charge of +2.0 nC from infinity to this point?

   [1 mark]

   • A9.0 × 10¹⁰ J
   • B3.6 × 10⁻⁷ J
   • C1.1 × 10⁻¹¹ J
   • D0 J

   (c)

   State what is meant by the absolute electric potential at a point in an electric field.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   Points A and B lie in the radial electric field of an isolated point charge of +3.0 nC in a vacuum. Point A is 0.20 m from the charge and point B is 0.50 m from it (ε₀ = 8.85 × 10⁻¹² F m⁻¹).

   (a)

   What is the potential difference between A and B?

   [1 mark]

   • A1.9 × 10² V
   • B90 V
   • C5.7 × 10² V
   • D81 V

   (b)

   A proton is released at A and moves directly away from the charge to B. What happens to its energy? (e = 1.60 × 10⁻¹⁹ C)

   [1 mark]

   • AIt loses 1.3 × 10⁻¹⁷ J of kinetic energy
   • BIt gains 2.2 × 10⁻¹⁷ J of kinetic energy
   • CIt gains 1.3 × 10⁻¹⁷ J of kinetic energy
   • DIt gains 8.6 × 10⁻¹⁸ J of kinetic energy

   (c)

   Point C is also 0.20 m from the charge. Explain why no work is done on a charge moved from A to C.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   In a region of space the electric potential falls uniformly with distance along a straight line, from 800 V at one point to 200 V at a second point 0.30 m further along the line. The field in this region is uniform.

   (a)

   Use E = −ΔV/Δr to calculate the magnitude of the electric field strength in this region, and state its direction relative to the change in potential.

   [3 marks]

   (b)

   An alpha particle of charge +3.2 × 10⁻¹⁹ C and mass 6.65 × 10⁻²⁷ kg is released from rest at the 800 V point. Calculate the work done on it by the field as it moves to the 200 V point and its speed there.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   An isolated metal sphere of radius 0.10 m carries a charge of +8.0 nC, which may be treated as a point charge at the centre of the sphere. The sphere is in a vacuum (ε₀ = 8.85 × 10⁻¹² F m⁻¹).

   (a)

   Describe how the electric field strength E and the electric potential V vary with distance r from the centre of the sphere, for r > 0.10 m, and explain how E and V are related by graphs of each against r.

   [6 marks]

   (b)

   Calculate the potential at the surface of the sphere and at 0.30 m from its centre, and hence the potential difference between these two points. A student estimates this potential difference as the surface field strength multiplied by 0.20 m. Explain whether this is an overestimate or an underestimate.

   [6 marks]

   Total for question 4: 12 marks

End of questions