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Question

Surface density of charge on a sphere of radius R in terms of electricity intensity E at a distance r in free space is ________.

(ϵ0= permittivity of free space)

A
ϵ0E(Rr)2
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B
ϵ0ERr2
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C
ϵ0E(rR)2
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D
ϵ0ErR2
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Solution

The correct option is C ϵ0E(rR)2
At distances greater than the radius from the center, the electric field due to a charged sphere is same as that of a point charge of same magnitude:

E=Q4πϵ0r2

Now, total charge and surface charge density are related by:

Q=4πR2σ

This gives:

σ=ϵ0E(rR)2

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