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
$\Rightarrow \frac{ kdq }{ R ^{2}}=\frac{ k }{ R ^{2}} \times \frac{ Qd }{2 \pi R }$
$\Rightarrow E =\frac{ KQd }{2 \pi R ^{3}}$
$\Rightarrow E \propto \frac{1}{ R ^{3}}$