Question

Two spheres of radii r and R carry charges q and Q respectively. When they are connected by a wire, there will be no loss of energy of the system if (a)qr=QR (b)qR=Qr (c)qr²=QR² (d) qR²=Qr²

Answer 1

Dear Student,

$$\begin{gathered} \mathrm{There}\mathrm{will}\mathrm{be}\mathrm{no}\mathrm{loss}\mathrm{of}\mathrm{energy}\mathrm{if}\mathrm{the}\mathrm{potential}\mathrm{of}\mathrm{the}\mathrm{spheres}\mathrm{is}\mathrm{the}\mathrm{same} \\ \mathrm{i}.\mathrm{e}.,\mathrm{if} \\ \mathrm{V}=\frac{\mathrm{q}}{4{\mathrm{\pi \epsilon }}_0\mathrm{r}}=\frac{\mathrm{Q}}{4{\mathrm{\pi \epsilon }}_0\mathrm{R}} \\ \mathrm{or},\frac{\mathrm{q}}{\mathrm{r}}=\frac{\mathrm{Q}}{\mathrm{R}} \\ \mathrm{Hence},\mathrm{qR}=\mathrm{Qr} \end{gathered}$$