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
$E=\frac{kQx}{{\left(R^2+x^2\right)}^{3/2}}$
At $x=R:E=\frac{kQ}{2\sqrt{2}{R}^2}$ directed towards the centre.

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