A-LevelPhysicsElectric fields9702/42 · May/June 2020 · Q710 Marks
A metal sphere of radius R is isolated in space. Point P is a distance x from the centre of the sphere, as illustrated in Fig. 7.1. The variation with distance x of the electric field strength E due to the charge on the sphere is shown in Fig. 7.2. [Figure 7.1] [Figure 7.2]
- (a)State what is meant by electric field strength.[2]
- (b)(i)Use Fig. 7.2 to determine the radius R of the sphere. Explain your working.[2]
- (b)(ii)Use Fig. 7.2 to determine the charge Q on the sphere.[3]
- (c)An α-particle is situated a distance 8.0 cm from the centre of the sphere. Calculate the acceleration of the α-particle.[3]
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Mark scheme
Marking points from the official mark scheme (May/June 2020). The mark or mark type is shown in brackets.
- [1] force per unit charge
- [1] (force on) positive charge
- [1] no electric field inside a conductor
- [1] R = 4.5 cm
- [1] E = Q / (4πε₀x²)
- [1] clear correct read-off of a pair of values of E and x
- [1] e.g. Q = 18 × 10⁵ × 4π × 8.85 × 10⁻¹² × (4.5 × 10⁻²)²
- [1] = 4.0 x 10⁻⁷ C or 4.1 × 10⁻⁷ C
- [1] At 8.0 cm, E = 5.75 × 10⁵ V m⁻¹
- [1] F = Eq and a = F/m
- [1] a = (5.75 × 10⁵ × 2 × 1.6 × 10⁻¹⁹) / (4 × 1.66 × 10⁻²⁷)
- [1] = 2.8 x 10¹³ m s⁻²
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