Question

A non-conducting 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

The correct option is A Directed towards the gap, inversely proportional to $R^3$.


If the gap is created, then net electric field at the centre is in a direction towards the gap because if the gap is filled then $E_{net}$ at centre $=0$
$E=\frac{Kq}{R^2}$
As charge is distributed along length $(q=\frac{Qd}{2\pi R})$
$E=\frac{KQd}{2\pi R^3}$
$E\propto R^{-3}$