A thin insulating rod is bent into a semicircular arc of radius a, and a total electric charge Q is distributed uniformly along the rod. Calculate the potential at the center of curvature of the arc if the potential is assumed to be zero at infinity.

Explanation:

We define the linear density of charge as:

     Where L is the rod's length, in this case the semicircle's length L = πr

The potential created at the center by an differential element of charge is:

          where k is the coulomb's constant

                     r is the distance from dq to center of the circle

Thus.

    Potential at the center of the semicircle

it may be wrong but i think its a

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