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Question

A sphere of radius R has a uniform distribution of electric charge in its volume. At a distance x from its centre, for x < R, the electric field is directly proportional to

A
1x2
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B
1x
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C
x
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D
x2
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Solution

The correct option is C x
Let sphere has uniform chare density \(\rho \left(=\frac{3 Q}{4 \pi R^3}\right) and E is the electric field at distance x from the centre of the sphere.
Applying Gauss law

E.4πx2=qϵ0=ρVϵ0=ρϵ0×43πx3
(V' = Volume of dotted sphere)
E=ρ3ϵ0xEx

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