Two concentric metallic shells of radius R & 2R, out of which the inner shell is having charge Q and outer shell is uncharged. If they are connected with a conducting wire, then

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Q amount of charge flow from inner to outer shell

Q/e number of electrons flow from outer to inner shell where $e = 1.6 \times 10^{- 19} C$

$\frac{{KQ}^{2}}{2 R}$ amount of heat is produced in the wire

$\frac{{KQ}^{2}}{4 R}$ amount of heat is produced in the wire

answer is A, B, C.

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Detailed Solution

Initially the system is shown in figure - 1. Initial energy stored in system is

$U_{i} = E n e r g y s t o r e d i n t h e s p a c e b e t w e e n t h e s h e l l s + E n e r g y s t o r e d i n t h e s p a c e o u t s i d e t h e o u t e r s h e l l = \frac{Q^{2}}{8 π ϵ_{0} R} = \frac{K Q^{2}}{2 R}$

As the two she U are connected the entire charge Q passes through wire and resides on outer shell, so that both the shells have same potential. Anal energy stored in system is,

$U_{f} = \frac{Q^{2}}{8 π ϵ_{0} \times 2 R} = \frac{K Q^{2}}{4 R}$