Physics (AS & A Level) · Oct / Nov 2016 · Paper 42 · Question 6
9702
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Two solid metal spheres A and B, each of radius 1.5 cm, are situated in a vacuum. Their centres are separated by a distance of 20.0 cm, as shown in Fig. 6.1. P sphere A sphere B x 20.0 cm 1.5 cm 1.5 cm Fig. 6.1 (not to scale) Both spheres are positively charged. Point P lies on the line joining the centres of the two spheres, at a distance x from the centre of sphere A. The variation with distance x of the electric field strength E at point P is shown in Fig. 6.2. 50 10 –10 –20 –30 –40 –50 20 30 40 0 0 4 2 6 10 14 18 8 12 16 20 x / cm E / N C–1 Fig. 6.2
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6(a)[3]
E = 0 or EA = (–)EB (at x = 11 cm) QA / x2 = QB / (20 – x) 2 = 112 / 92 QA / QB or ratio = 1.5 [3]
or E ∝ Q because r same or E = Q / 4πε0r2 and r same (B1) QA / QB = 48 / 32 (C1) QA / QB or ratio = 1.5 (A1)
6(b)(i)[3]
for max. speed, ∆V = (0.76 – 0.18) V or ∆V = 0.58 V q∆V = ½mv2 2 × (1.60 × 10–19) × 0.58 = ½ × 4 × 1.66 × 10–27 × v2 v2 = 5.59 × 107 v = 7.5 × 103 m s–1 [3]
6(b)(ii)[2]
∆V = 0.22 V 2 × (1.60 × 10–19) × 0.22 = ½ × 4 × 1.66 × 10–27 × v2 v2 = 2.12 × 107 v = 4.6 × 103 m s–1 [2]
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