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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 R3.
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B
Directed towards the gap, inversely proportional to R2.
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C
Directed away from the gap, inversely proportional to R3.
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D
Directed away from the gap, inversely proportional to R2.
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Solution

The correct option is A Directed towards the gap, inversely proportional to R3.

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 Enet at centre =0
E=KqR2
As charge is distributed along length (q=Qd2πR)
E=KQd2πR3
ER3

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