A conducting sphere of radius R carrying charge Q lies inside an uncharged conducting shell of radius 2 R . If they are joined by a metal wire, the amount of heat that will be produced is

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The capacitances of two are C 1 ​ = 4 π ε 0 ​ R and C 2 ​ = 4 π ε 0 ​ ( 2 R ) Initial energy = E i ​ = 2 C 1 ​ Q 2 ​ Final energy = E f ​ = 2 C 2 ​ Q 2 ​ Heat produced = E i ​ − E f ​ ​ = 2 Q 2 ​ [ 4 π ε 0 ​ R 1 ​ − 2 × 4 π ε 0 ​ R 1 ​ ] = 4 π ε 0 ​ 1 ​ ⋅ 2 R Q 2 ​ [ 1 − 2 1 ​ ] = 4 π ε 0 ​ 1 ​ ⋅ 4 R Q 2 ​ ​

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