A cylindrical capacitor is composed of an inner conducting cylindrical shell whi

Question

A cylindrical capacitor is composed of an inner conducting cylindrical shell which has a radius r_1 and ab outer shell with a radius r_2. A positive charge Q is placed on the inner shell while a negative charge - Q is placed on the outer shell. Two conducting cylindrical shells have same length L. Find the analytic expression for the capacitance of the cylindrical capacitor. A particle with mass m and positive charge q is placed right next to the inner shell with 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. The cylindrical capacitor is designed to store 1 nC of charge when a 100 V battery is connected. For r_1 = 5 cm and L = 10 m, find r_2 to satisfy the design criteria.

Explanation / Answer

a) C = 2*pi*epsilon*L/ln(r2/r1)

b) Let v is the speed of charged particle at outer plate.

workdone on charged particle = q*delta_V

0.5*m*v^2 = q*Q/C

v = sqrt(2*q*Q/(m*C))

c) C = Q/delta_V

= 1*10^-9/100

= 1*10^-7 F

C = 2*pi*epsilon*L/ln(r2/r1)

ln(r2/r1) = 2*pi*epsilon*L/C

= 2*pi*8.854*10^-12*10/(1*10^-7)

ln(r2/r1) = 0.00556

r2 = r1*e^0.00556

= 5*e^0.00556

= 5.028 cm <<<<<<<-------Answer

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