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Question

# In a system of two concentric spherical conducting shells charge q is given to both inner and outer shells as shown in figure. Inner shell is connected to earth by a switch. Find the amount of heat produced when switch is closed.

A
kq24a
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B
kq28a
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C
9kq28a
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D
6kq27a
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Solution

## The correct option is C 9kq28aInitial potential energy of the system Uinitial=∑Uself+Uinteraction Substituting the values, ⇒Uinitial=kq22a+kq22×2a+(kq22a) ∴Uinitial=5kq24a When the inner sphere is grounded let's assume q′ be the final charge on inner sphere such that electric potential on it, Vinner=0, ⇒kq′a+kq2a=0 ⇒q′=−q2 Final energy Ufinal of the system: Ufinal=∑Uself+Uinteraction ⇒Ufinal=kq′22a+kq22(2a)+kq′2aq ⇒Ufinal=kq28a+kq24a−kq24a ⇒Ufinal=kq28a Amount of Heat produced =(Ui−Uf) =5kq24a−kq28a =9kq28a Hence, option (c) is the correct answer.

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