The concentric, conducting spherical shells X, Y and Z with radii r, 2 r and 3 r , respectively. X and Z are connected by a conducting wire and Y is uniformly charged to charge Q as shown in figure. Charges on shells X and Z will be

Step-by-step solution

Let charges on X and Z be q_x and q_Z By conservation of charge, q_x+q_z=0 q_z=-q_x aligned V_x & = 1 4 ₀ [ q_x r + Q 2 r + q_z 3 r ] V_z & = 1 4 ₀ [ q_x 3 r + Q 3 r + q_z 3 r ] aligned Since, X and Z are connected. V_x=V_Z aligned & & q_X r + Q 2 r + q_Z 3 r & = q_X 3 r + Q 3 r + q_Z 3 r & & 2 q_X 3 & = -Q 6 & & q_X & = -Q 4 & & q_X+q_Z & =0 q_Z=-q_X & & & = Q 4 aligned