Question

A uniformly charged insulating rod of length 14 cm is bent into the shape of a semicircle. if the rod has a total charge of -7.5 C. find the magnitude and direction of the electric field at the center of the semicircle.

I'm not sure where to start or what to do. what formula is used?

Answer 1

You know the formula for E from any segment dL (dL contains dq). You have to integrate around the semicircle to get E. Actually, it is easy as a vector, because you use arguments of symettry to just integrate the components of E directed along the axis of symettry, as the E perpendicular will cancel out. You will be integrating a sin/cos function of the angle, and it becomes trivial.