9702/42/M/J/15: (a) Define electric potential at a point.
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(b) Two positively charged metal spheres A and B are situated in a vacuum, as shown in Fig. 5.1. A point P lies on the line joining the centres of the two spheres and is a distance x from the surface of sphere A. The variation with x of the electric potential V due to the two charged spheres is shown in Fig. 5.2.
(i) State how the magnitude of the electric field strength at any point P may be determined from the graph of Fig. 5.2.
(ii) Without any calculation, describe the force acting on a positively charged particle placed at point P for values of x from x = 0 to x = 10 cm.
(c) The positively charged particle in (b)(ii) has charge q and mass m given by the expression. Initially, the particle is at rest on the surface of sphere A where x = 0. It then moves freely along the line joining the centres of the spheres until it reaches the surface of sphere B.
(i) On Fig. 5.2, mark with the letter M the point where the charged particle has its maximum speed.
(ii) 1. Use Fig. 5.2 to determine the potential difference between the spheres.
2. Use your answer in (ii) part 1 to calculate the speed of the particle as it reaches the surface of sphere B. Explain your working.
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