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Question: An insulating solid sphere of radius R is charged in a non-uniform manner such that volume charge de...

An insulating solid sphere of radius R is charged in a non-uniform manner such that volume charge density ρ=Ar\rho = \frac{A}{r}, where A is a positive constant and r is the distance from centre. Potential difference between centre and surface of sphere is –

A

AR∈0\frac{AR}{\in_{0}}

B

AR4∈0\frac{AR}{4 \in_{0}}

C

ARπ∈0\frac{AR}{\pi \in_{0}}

D

AR2∈0\frac{AR}{2 \in_{0}}

Answer

AR2∈0\frac{AR}{2 \in_{0}}

Explanation

Solution

E × 4pr2 = qϵ0\frac { \mathrm { q } } { \epsilon _ { 0 } }

E × 4pr2 = ∫0rAr\int _ { 0 } ^ { r } \frac { A } { r } × 4pr2 dr

E = A2∈0\frac { \mathrm { A } } { 2 \in _ { 0 } }

Potential difference = E × d

=