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Q.

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

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a

none

b

$(σ / ε_{0}) [a + b - c]$

c

$(σ / ε_{0}) [a - b + c]$

d

$(σ / ε_{0}) [b - a - c]$

answer is C.

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Detailed Solution

Potential on sphere A is equal potential at centre.

Which is equal to potential at centre due to A + B + C

$= \frac{(- σ) a}{ε_{0}} + \frac{σb}{ε_{0}} + \frac{(- σ) c}{ε_{0}} = \frac{σ}{ε_{0}} [b - a - c]$

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