Question

A nonconducting ring of radius $R$ has uniformly distributed positive charge $Q.$ A small part of the ring, of length $d$, is removed $(d<<R)$. The electric field at the centre of the ring will now be :

• A. Directed towards the gap, inversely proportional to $R^3$
• B. Directed towards the gap, inversely proportional to $R^2$
• C. Directed away from the gap, inversely proportional to $R^3$
• D. Directed away from the gap, inversely proportional to $R^2$

Answer 1

Answer: (A)

Electric field due to part 'd' is
$\Rightarrow \frac{kdq}{R^2}=\frac{k}{R^2}\times \frac{Qd}{2\pi R}$
$\Rightarrow E=\frac{KQd}{2\pi R^3}$
$\Rightarrow E\propto \frac{1}{R^3}$