Question

1. A hollow conducting sphere of radius R has a charge Q placed on its surface. A point charge Q1 is placed at a distance d> R from the center of the sphere. a) Using the method of superposition, find a combination of two image charges inside the sphere that result in the correct electric field and potential outside the sphere. b) What is the force between the sphere and the point charge? What is the force whern 0, and for what value of Q is the force zero?

Answer 1

The answer is explained as above. The answer for last part of (b) is the value for Q donot exist for Q1 is nonzero as it induces the charge in conductor non uniformly and net force is nonzero. Thank you, please like the answer.

(a) net electric field = E_Q + E_Q_1 outside sphere E_Net_p^bar = 1/4 pi E_0[Q/ Vertical-bar r_1^vector Vertical-bar ^3 r_1^vector + Q_1/ Vertical-bar r_2^vector Vertical-bar ^3 r_2^vector] Net potential v_p = 1/4 pi E_0[Q/ Vertical-bar r_1 Vertical-bar + Q_1/ Vertical-bar r_2^vector Vertical-bar ] (b) F^vector = 1/4 pi E_0 (Q Q_1/d^2), for Q = 0, F notequalto 0 as non uniform charge is induced on the conducting sphere For F^vector = 0, Q = it is not defined as the force is non zero for Q_1 notequalto c The answer is explained as above. The answer for last part of (b) is the value for Q donot exist for Q1 is nonzero as it induces the charge in conductor non uniformly and net force is nonzero.