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Question

Three concentric metallic spherical shells A, B and C of radii a, b and c (a<b<c) have surface charge densities σ, +σ, and σ respectively. The potential of shell A is:

A
σϵ0(a+bc)
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B
σϵ0(ab+c)
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C
σϵ0(bac)
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D
None
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Solution

The correct option is C σϵ0(bac)

Let, the charge on shells A, B and C are qA, qB and qC respectively.

So, the net potential on A:

VA=14πϵ0(qCc+qBb+qAa)

According to problem
qA=σ4πa2
qB=+σ4πb2
qC=σ4πc2

Substituting the values in the above equation we get,

VA=14πϵ0[σ4πc2c+σ4πb2bσ4πa2a]

VA=σϵ0(bca)

Hence, option (c) is the correct answer.

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