Two isolated conducting spheres each of radius R and carrying charges Q and 2Q. They are connected by a wire. Find the amount of heat produced during the transfer of charge from one sphere to other sphere

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kQ²/2R

kQ²/R

kQ²/4R

2kQ²/4R

answer is A.

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Detailed Solution

Initial energy : $U_{1} = \frac{Q^{2}}{2 C} + \frac{(2 Q)^{2}}{2 C} = \frac{5 Q^{2}}{2 C}$

Final energy : $U_{2} = 2 (\frac{(3 Q / 2)^{2}}{2 C}) = \frac{9 Q^{2}}{4 C}$

Heat produced $= U_{1} - U_{2} = \frac{5 Q^{2}}{2 C} - \frac{9 Q^{2}}{4 C}$

$= \frac{Q^{2}}{4 C} = \frac{Q^{2}}{4 \times 4 {πε}_{0} R} = \frac{{kQ}^{2}}{4 R}$

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