Question

A nonconducting rod with a uniformly distributed charge +Q. The rod forms a 10/24 of circle with radius R and produces an electric field of magnitude Earc at its center of curvature P. If the arc is collapsed to a point at distance R from P ,by what factor is the magnitude of the electric field at P multiplied?

Answer 1

Kinda like this question. If the rod is collapsed at a point at distance \(R\) from the point, then it can be treated as a point charge producing an electric field of \(\frac{kQ}{R^2}\).

If it is an arc, then we'll have to use calculus. 10/24th of a circle means that an angle of 150 degrees is subtended at the center.