Question

A ring of radius $R$ is having two charges $q$ and $2q$ distributed on its two half parts as shown in the figure below. Find the electric potential at a point on its axis at a distance $2\sqrt{2}R$ from its center.

$[k=\frac{1}{4\pi {\epsilon }_0}]$

• A. $\frac{kq}{3R}$
• B. $\frac{3kq}{R}$
• C. $\frac{kq}{R}$
• D. None of these

Answer 1

The correct option is C $\frac{kq}{R}$


Distance of point $\text{P}$ from periphery of ring is,

$d=\sqrt{R^2+(2\sqrt{2}R{)}^2}=3R$

$\text{Electric potential at point P = potential due to upper half +potential due to lower half}$

$E_P=\frac{kq}{3R}+\frac{2kq}{3R}$

$\Rightarrow E_P=\frac{3kq}{3R}$

$\therefore E_P=\frac{kq}{R}$

Hence, option (c) is the correct answer.