(b) An isolated spherical conductor has charge q, as shown in Fig. 6.1. [Figure 6.1] Point P is a movable point that, at any one time, is a distance x from the centre of the sphere. The variation with distance x of the electric potential V at point P due to the charge on the sphere is shown in Fig. 6.2. [Figure 6.2] Use Fig. 6.2 to determine

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2017). The mark or mark type is shown in brackets.

1. [1] (a) electric field lines are radial/normal to surface (of sphere)
2. [1] (a) electric field lines appear to originate from centre (of sphere)
3. [1] (b)(i) tangent drawn at x = 6.0cm and gradient calculation attempted
4. [2] (b)(i) E = 9.0 × 10⁴ NC⁻¹ (1 mark if in range ±1.2; 2 marks if in range ±0.6)
5. [1] (b)(i) or correct pair of values of V and x read from curved part of graph and substituted into V = q/4πεx
6. [1] (b)(i) to give q = 3.6 × 10⁻⁸C
7. [1] (b)(i) (then E = q/4πεx² and x = 6cm gives) E = 9.0 × 10⁴ NC⁻¹
8. [1] (b)(i) or (E = q/4πεx² and V = q / 4πεx and so) E = V/x
9. [1] (b)(i) giving E = 5.4 × 10³/0.060
10. [1] (b)(i) = 9.0 × 10⁴ NC⁻¹
11. [1] (b)(ii) (R =) 2.5 cm
12. [1] (b)(ii) potential inside a conductor is constant or field strength inside a conductor zero (so gradient is zero)