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# The line charge density of a semi - circular ring of radius r is a .find electric field intensity at the centre of the ring ? What is the total charge of an electric dipole?

3 years ago

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@ ...

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)