Question

A ring of radius $R$ has charge $-Q$ distributed uniformly over it. A charge $q$ is placed at the centre of the ring such that the electric field becomes zero at a point on the axis of the ring distant $R$ from the centre of the ring. The value of charge $q$ is

• A. $\frac{Q}{2} \sqrt{3}$
• B. $\frac{Q}{4} \sqrt{2}$
• C. $\frac{Q}{3} \sqrt{2}$
• D. $\frac{Q}{4} \sqrt{3}$

Answer 1

Answer: (B)

Electric field at point $P$ due to charge of ring is
$E=\frac{k Q x}{\left(R^{2}+x^{2}\right)^{3 / 2}}$
At $x=R: E=\frac{k Q}{2 \sqrt{2} R^{2}}$ directed towards the centre.

Electric field at $P$ due to centre charge: $\frac{k q}{R^{2}}$
For net field to be zero at $P$ :
$\frac{k q}{R^{2}}=\frac{k Q}{2 \sqrt{2} R^{2}} $
$\Rightarrow q=\frac{Q}{2 \sqrt{2}}=\frac{Q}{4} \sqrt{2}$