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Q.

Three concentric spherical shells have radii a, band c (a < b < c) and have surface charge densities σ, -σ and σ respectively. If VA, VB and VC denote the potentials of the three shells, then for c = a + b, we have :

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a

VC=VB=VA

b

VC=VA ≠VB

c

VC=VB≠VA

d

VC≠VB=VA

answer is B.

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Detailed Solution

VA=kσ x 4πa2a+k-σ x 4πb2b+kσ x 4πc2c       =4πkσ(a-b+c)VB=kσ x 4πa2b+k-σ x 4πb2b+kσ x 4πc2c       =4πkσ(a2b-b+c)VC=kσ x 4πa2c+k-σ x 4πb2c+kσ x 4πc2c       =4πkσ(a-b+c)⇒VA=VC≠VB
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