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Question

Three concentric spherical metallic shells A, B and C of radii a,b and c (a<b<c) have charge densities σ,−σ and σ respectively. If the shells A and C are at the same potential then the relation between a, b and c is :

A
a+b+c=0
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B
a+c=b
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C
a+b=c
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D
a=b+c
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Solution

The correct option is C a+b=c

VA=σ4πa24πϵ0a+(σ)4πb24πϵ0b+σ4πc24πϵ0c

=σϵ0(ab+c)

Similarly, VC=σϵ0(a2cb2c+c)

But VA=VC

ab+c=a2b2c+c

Therefore, a+b=c


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