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Question

# A solid conducting sphere of radius a having a charge q is surrounded by a concentric conducting spherical shell of inner radius 2a and outer radius 3a as shown in figure. Find the amount of heat produced when switch is closed(K=14πε0)

A
K=kq22a
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B
K=kq23a
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C
K=kq24a
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D
K=kq26a
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Solution

## The correct option is C K=kq24aCapacitance of a spherical capacitor having inner radius of sphere a and radius of outer sphere b is :C=abK(b−a)b→∞C=akAnd energy of capacitor =q22CBefore closing the switch charge distribution is given byTotal energy of system = Energy of capacitor (1) + Energy of capacitor (2)Capacitance of 1st1st capacitor C1=a×2aK(2a−a)=2aKcapacitance of 2nd capacitor is C2=3aKtotalenergy=q22(2aK)+q22(3aK)totalenergy=Kq24a+Kq26aAfter closing the switch charge distribution istotalenergyfinal=q22(3aK)=Kq26aΔTE=TEf−TEi=Kq26a−(Kq26a+Kq24a)=−Kq24aheatproduced=+Kq24aOption C is correct.1t1capacitor

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