Question

A point charge q is kept at a distance of 2R from centre of an uncharged spherical shell of radius R. The potential at centre of the shell due to charges induced on shell is

• A. $\frac{q}{4\pi E_{0}R}$
• B. $\frac{q}{4\pi E_{0}2R}$
• C. $\frac{-q}{4\pi E_{0}R}$
• D. Zero

Answer 1

The correct option is C $\frac{-q}{4\pi E_{0}R}$

Charge $=q$

distance $=2R$

radius $=R$

$V=$ Potential at centre of the shell due to charge induced on shell.

As the electric field inside a conductor is zero. The electrostatic potential is constant it. The potential at centre will be the potential of entire conductor. The entire charge of conductor is on surface $N$.

Now, $V=\frac{-1}{4\pi {ϵ}_0}\frac{q}{R}$

The $(-Ve)$ sign due to spherical shell of centre (inside).