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A cylindrical capacitor is composed of an inner conducting cylindrical shell which has a radius r and the outer shell with a radius 12.

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A cylindrical capacitor is composed of an inner conducting cylindrical shell which has a radius r and the outer shell with a radius 12. Positive charge Q is placed on the inner shell while negative charge -Q is on the outer shell. Two conducting cylindrical shells have same length L. (a) Find the expression for the capacitance of the cylindrical capacitor. (b) A particle that has mass m and positive charge q is placed right next to the inner shell with a zero initial velocity. The particle will be repelled by the positively charged inner shell. Find the velocity of the particle when it reaches the outer shell. (c) The cylindrical capacitor is designed to store 1 nC of charge when 10V battery is connected. For r = 5 cm and L = 1 m, find r to satisfy the design criteria.

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