(b) A positive point charge +Q is positioned at a fixed point X and an identical positive point charge is positioned at a fixed point Y, as shown in Fig. 6.1. X +Q A 2.5 cm 10.0 cm Fig. 6.1 B Y +Q 2.5 cm The charges are separated in a vacuum by a distance of 10.0 cm. Points A and B are on the line XY. Point A is a distance of 2.5cm from X and point B is a distance of 2.5cm from Y. The electric field strength at point A is 4.1 × 10⁻⁵ Vm⁻¹. (ii) On Fig.6.2, sketch the variation of the electric field strength E with distance d from A to B, along the line AB. 5 E/10⁻⁵ V m⁻¹ 4- 3 2 1 0+ 0 -1 -2- -3- -4- -5- 1 2 3 d/cm 4 5 Fig. 6.2
- (a)State one similarity and one difference between the electric field lines and the gravitational field lines around an isolated positively charged metal sphere.[2]
- (b)(i)Calculate charge +Q.[3]
- (b)(ii)On Fig.6.2, sketch the variation of the electric field strength E with distance d from A to B, along the line AB.[2]
- (b)(iii)A small positive charge is placed at A. The electric field causes this charge to move from rest along the line AB. Describe the acceleration of the charge as it moves from A to B.[2]
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Mark scheme
Marking points from the official mark scheme (Feb/Mar 2017). The mark or mark type is shown in brackets.
- [B1] similarity: lines are radial/greater separation of lines with increased distance from the sphere
- [B1] difference: gravitational lines directed towards sphere and electric lines directed away from sphere
- [C1] E = Q / 4πε₀r² or E = kQ / r² with k defined/substituted in
- [C1] 4.1 × 10⁻⁵ = [Q / (4π × 8.85 ×10⁻¹² × 0.025²)] – [Q / (4π × 8.85 × 10⁻¹² × 0.075²)]
- [A1] Q = 3.2 x 10⁻¹⁸ C
- [B1] smooth curve with gradient decreasing starting at (0, 4.1 × 10⁻⁵) to d-axis at (2.5, 0)
- [B1] smooth curve with gradient increasing from (2.5, 0) ending at (5, – 4.1 × 10⁻⁵)
- [B1] acceleration decreases (to zero at mid-point)
- [B1] then acceleration increases in the opposite direction/increasing negative acceleration
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