PHYSICS · Subjective · A Level · Physics · Fields and their consequences · Fields and their consequences
Problem
A regular polygon of n sides, each of length a, has identical point charges +Q at every vertex except one. The vacant vertex is labelled A and the centre of the polygon is O.
(a) Show that the distance R between any vertex and O is R=2sin(nπ)a.
(b) Treating each charge individually, derive an expression for the magnitude of the net electric field at O due to the (n−1) charges present.
(c) Using your result, find the magnitude of the field at the centre when n=8, a=0.25m and Q=5μC.