Question

An electric charge Q is uniformly distributed around a semi-circle of radius a.Calculate the electric potential at it's center

Answer 1

Answer:

The semi circular charge with radius R is shown in blue. The incremental arc element ds has a charge, dq = rho R ds where rho is the linear charge density for the differential arc length. By symmetry we can see that Ex = integral(dEx) from 0 to Pi is going to equal zero. But not Ey.

Answer 2

Answer:

Go through the Picture attached . The easiest way to add potential due to all the elementary charges is to integrate them taking Limit