Electric Potential at a Point in Space Due to a Point Charge Q
A sphere of r...
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 Cx 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=ρ3ϵ0x⇒E∞x