a semicircular rod has uniform charge density Lambda find an

a semicircular rod has uniform charge density Lambda. find an expression for the potential at the \"x\" on the y-axis.

Solution

Coordinates of point b = (0, b)

at @, coordinates (Rcos@, Rsin@)

charge of small d@ arc part. dq = R lambda d@

r = sqrt[ (Rcos@)^2 + (Rsin@ - b)^2 ]

dV = kdq/r

dV = k R lambad d@ / sqrt[(Rcos@)^2 + (Rsin@ - b)^2]

V = intrgral of k R lambad d@ / sqrt[(Rcos@)^2 + (Rsin@ - b)^2]  

@ is from 0 to pi .

ANs (d)