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# A solid conducting sphere of radius ′a′ having charge q is surrounded by a concentric conducting spherical shell of inner radius 2a and outer radius 3a as shown in figure. If the amount of heat produced when switch is closed is α(Kq224a). Fill the value of α.

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Solution

## Capacitance of a spherical capacitor having inner radius of sphere a radius of outer sphere b isC=abK(b−a)As b→∞C=aKAnd energy of capacitor =q22CBefore closing the switch charge distribution is given by.Total energy of system = Energy of capacitor (1)+ Energy of capacitor (2)Capacitance of 1st capacitor C1=a×2aK(2a−a)=2aKCapacitance of 2nd capacitor C2=3aKTotal energy =q22(2aK)+q22(3aK)T.Ei=Kq24a+Kq26aAfter closing the switch charge distribution is as shown in Fig 3Total energy =0+q22(3aK)T.Ef=Kq26a△T.E=−Kq24a=T.Ef−T.EfThus heat produced =+Kq24aIf the amount of heat produced when switch is closed is 6(Kq224a)Then α=6

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