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 we fill the gap then there will be no electric field at the center of ring
This signifies that electric field due to rest ring is equal to electric field due to gap and opposite in direction
so electric field due to gap=$\frac{Kq}{R^2}$
$q=\frac{Qd}{2\pi R}$
thus electric field E=$\frac{KQd}{R^3}$
Hence E will be inversely proportional to $R^3$ and direction will be toward the gap