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Question

# Three concentric spherical metallic shells A,B,andC of radii a,b,andc(a<b<c) have charge densities of σ,−σandσ respectively. Match the column and select the correct answer using the codes given belowCodes :P Q R S(A)2314(B)1423(C)4123(D)2341

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Solution

## Now charge on sphere of radius a is σ4πa2charge on sphere of radius b is −σ4πb2charge on sphere of radius c is σ4πc2potential on surface is given by V=q/4πϵoRNow for A VA=σa/ϵoSimilarly on surface of all sphere potential due to themselves is σ/ϵoNow on surface of potential is due to sphere A ,B, and Ctherefore, Therefore, VA=potential due to (A+B+C) at (r=a) isσ/ϵo(a−b+c)Similarly, since for sphere B VB= potential due to (A+B+C) at (r=b) isσ/ϵo(a2/b−b+c)Now similarly for sphere C VC=σϵo(a2/c−b2/c+c)and field at surface of a is σ/ϵo

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