First slide

Pontial due to

Question

A thin spherical conducting shell of radius fi has a charge q. Another charge Q is place at the centre of the shell. The electrostatic potential at a point P a distance R/2 from the centre of the shell is

Easy

A

$\frac{(q + Q)}{4 {πε}_{0}} \frac{2}{R}$
B

$\frac{2 Q}{4 {πε}_{0} R}$
C

$\frac{2 Q}{4 {πε}_{0} R} - \frac{2 q}{4 {πε}_{0} R}$
D

$\frac{1}{4 {πε}_{0}} \cdot \frac{1}{R} \times (q + 2 Q)$

Solution

The electrostatic potential on the surface of spherical shell of fi having a charge g is given by
$V_{1} = \frac{1}{4 {πε}_{0}} \cdot \frac{q}{R}$
This potential is same at point P. When charge Q is placed at the can be, then potential at P
$V_{2} = \frac{1}{4 {πε}_{0}} \cdot \frac{Q}{(R / 2)}$
$∴ Total potential at P$
$\begin{array}{l} V = V_{1} + V_{2} = \frac{1}{4 {πε}_{0}} [\frac{q}{R} + \frac{2 Q}{R}] \\ = \frac{1}{4 {πε}_{0}} \times \frac{1}{R} \times (q + 2 Q) \end{array}$

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