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Question

A ring of radius R has charge -Q distributed uniformly over it. Calculate the charge that should be placed at the center of the ring such that the electric field becomes zero at a point on the axis of the ring at distant R from the center of the ring

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Solution

Electric field at point P due to charge of ring is

E=kQx(R2+x2)3/2

At x=R,E=kQ22R2 directed toward the center.

Electric field at P due to charge at center kq/R2

For net field to be zero at P.

kqR2=kQ22R2 or q=Q22


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