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Question: A point charge is placed at a distance r from centre of a conducting neutral sphere of radius R(r \>...

A point charge is placed at a distance r from centre of a conducting neutral sphere of radius R(r > R). The potential at any point P inside the sphere at a distance r1 from the point charge due to induced charge of the sphere is given by [k=14π∈0]\left\lbrack k = \frac{1}{4\pi \in_{0}} \right\rbrack-

A

kqr1\frac{kq}{r_{1}}

B

kqr−kqr1\frac{kq}{r} - \frac{kq}{r_{1}}

C

kqr\frac{kq}{r}

D

−kqR- \frac{kq}{R}

Answer

kqr\frac{kq}{r}

Explanation

Solution

Potential at centre = Vq + Vinduced

= Vq + 0

= Vq =

Potential at P = potential at C

Vq + Vinduced =

Vinduced =– q4π∈0r1\frac { \mathrm { q } } { 4 \pi \in _ { 0 } \mathrm { r } _ { 1 } } = kqr\frac { \mathrm { kq } } { \mathrm { r } } – kqr1\frac { \mathrm { kq } } { \mathrm { r } _ { 1 } }