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consider a small element of length dl on the ring ..let @ is the angle be radious vector with base then angle substended
by this element at center is d@ ...
arc/radius = @
dl = Rd@ ..............1
let charge dencity = p then charge of this element is dq
dq = p(dl) = pRd@ ..............2
electric field due to this element at center dE (magnitude)= kdq/R2
dE = Kdq/R2cos@ (i) + kdq/R2sin@ (-j) with direction
dE = kdq/R2[cos@i - sin@j]
dE = kp/R [ cos@d@ (i) - sin@d@ (j) ] lim from 0 to pi
E = kp/R [ -2j ]
now we have p (charge per unit length) = Q/piR so
E = 2kQ/piR2 (-j)
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