Question

Charge Q is distributed uniformly on length of a wire. It is bent in the form of a semicircular ring. Find the electric field at the centre of the ring.

A

B

C

D

Hard

Solution

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Correct option is D)

Consider two small elements of length each charge on each element. If is the line charge density, . as wire is bent in the form of semicircular ring.
Hence , 
.  
Here sine component of the field at center cancel out and  only cosine will contribute the filed.
thus,
or     as

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