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Question

# Two concentric spheres kept in air have radii 'R' and 'r'. They have similar charge and equal surface charge density 'σ'. The electric potential at their common centre is ______. (ϵ0=permittivity of free space)

A
σ(R+r)ϵ0
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B
σ(Rr)ϵ0
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C
σ(R+r)2ϵ0
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D
σ(R+r)4ϵ0
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Solution

## The correct option is B σ(R+r)ϵ0The potential at the centre of a sphere of radius r and surface charge q isV=14πϵ0qrV=rϵ0(q4πr2)=σrϵ0The potential at centre of two concentric spheres of radii r and R is addition of individual potentials by each shell.V=σ(R+r)ϵ0

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