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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 below
Codes :
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 σ4πa2
charge on sphere of radius b is σ4πb2
charge on sphere of radius c is σ4πc2
potential on surface is given by V=q/4πϵoR
Now for A VA=σa/ϵo
Similarly on surface of all sphere potential due to themselves is σ/ϵo
Now on surface of potential is due to sphere A ,B, and C
therefore, Therefore, VA=potential due to (A+B+C) at (r=a) isσ/ϵo(ab+c)
Similarly, since for sphere B VB= potential due to (A+B+C) at (r=b) isσ/ϵo(a2/bb+c)
Now similarly for sphere C VC=σϵo(a2/cb2/c+c)
and field at surface of a is σ/ϵo


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