An electric charge Q is uniformly distributed around a semi-circle of radius a. Calculate the electric potential at the centre of this semi-circle.

Explanation

Q is total charge distributed over given semi-circle.
`therefore` Charge per unit length `=(Q)/(pi R)`
Electric potential at O due to small element PQ is dV and dV= kdq `(because dq= (Q)/(pi) xx dl)`

Now, integrate both sides with proper limit, we get
`underset(0)overset(V)int dV = (kQ)/(pi^(2)) underset(0)overset(pi)int dl rArr V= (kQ)/(pi^(2)) xx pi rArr V= kQ`