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Question

# In a hypothetical situation if a point charge q is brought from infinity (slowly so that heat developed in the shell is negligible) and placed at the centre of a conducting neutral spherical shell of inner radius a and outer radius b, then work done by external agent is calculated to be ka2na−kq22b .Find the value of n (Give integer value)

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Solution

## When charge is at infinity, potential energy of the system is zero. So, Ui=0 When charge is placed at centre, induced Charges will appear on the shell as shown The final potential energy of the system will be: Uf = Self energy of S1 and S2 +Interaction energy of S1 and S2 +Interaction energy of q with S1 +Interaction energy of q with S2 Uf=(K(−q)22a+K(q)22b)+(K(−q)(q)b)+(K(−q)qa)+Kq2b ⇒Uf=kq22a+kq22b−kq2b−kq2a+kq2b So, Work done W=Uf−Ui W=kq22b−kq22a Comparing with the data given in the question we get,n=2 Accepted answer : 2

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