A-LevelPhysicsElectric fields9702/42 · Oct/Nov 2020 · Q511 Marks

An isolated solid metal sphere of radius 0.15m is situated in a vacuum, as illustrated in [Figure 5.1]. The electric field strength at the surface of the sphere is 84Vm⁻¹. Determine:

(a)(i)State what is meant by a field of force.[2]
(a)(ii)State one similarity and one difference between the electric field due to a point charge and the gravitational field due to a point mass.[2]
(b)(i)the charge Q on the sphere[2]
(b)(ii)the electric field strength at point P, a distance x = 0.45m from the centre of the sphere.[2]
(c)Use information from (b) to show, on the axes of [Figure 5.2], the variation of the electric field strength E with distance x from the centre of the sphere for values of x from x = 0 to x = 0.45 m.[3]

This question uses a diagram from the original paper, which isn't shown here. Open the full paper from the past papers archive to see it.

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2020). The mark or mark type is shown in brackets.

[B1] region (of space)
[B1] where a particle experiences a force
[B1] similarity – any one point from: • both have an inverse square variation • both decrease with distance • both are radial
[B1] difference - any one point from: • gravitational field always towards (the mass) • electric field can be towards or away from (the charge)
[C1] E = Q/ 4πε₀x²
[A1] = 4π × 8.85 × 10⁻¹² × 84 × 0.15², = 2.1 x 10⁻¹⁰ C
[C1] E = 84 × (0.15/0.45)² OR E = (2.1 × 10⁻¹⁰) / (4π × 8.85 × 10⁻¹² × 0.45²)
[A1] E = 9.3 V m⁻¹
[B1] line at E = 0 from x = 0 to x = 0.15 m
[B1] smooth curve with decreasing negative gradient throughout, from x = 0.15 m to x = 0.45 m, passing through (0.15, 84)
[B1] line passing through (0.45, 9.3)

On Oracle Prep you can write or photograph your own answer and have it marked by AI against this mark scheme, with feedback on what you missed.