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(B) Initial potential energy of the system $(U_i)$: $U_i = U_{	ext{sphere}} + U_{	ext{shell}} + U_{	ext{interaction}}$ $U_i = \frac{KQ^2}{2a} + \fr

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$\frac{KQ^2}{4a}$

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(B) Initial potential energy of the system $(U_i)$: $U_i = U_{	ext{sphere}} + U_{	ext{shell}} + U_{	ext{interaction}}$ $U_i = \frac{KQ^2}{2a} + \frac{KQ^2}{2(2a)} + \frac{KQ \cdot Q}{2a} = \frac{KQ^2}{2a} + \frac{KQ^2}{4a} + \frac{KQ^2}{2a} = \frac{5KQ^2}{4a}$ When connected, the total charge $2Q$ resides on the outer shell because the inner sphere is at a higher potential. Final potential energy of the system $(U_f)$: $U_f = \frac{K(2Q)^2}{2(2a)} = \frac{4KQ^2}{4a} = \frac{KQ^2}{a}$ Heat produced $(H)$ = $U_i - U_f$ $H = \frac{5KQ^2}{4a} - \frac{KQ^2}{a} = \frac{KQ^2}{4a}$

The figure shows a solid metal sphere of radius $a$ surrounded by a concentric thin metal shell of radius $2a$. Initially, both have charges $Q$ each. When the two are connected by a conducting wire as shown in the figure, the amount of heat produced in this process will be:

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