Identical point charges q are fixed at each of the n vertices of a regular n-sided…
PHYSICS · Multi-part · A Level · Physics · Fields and their consequences · Fields and their consequences
Problem
Identical point charges q are fixed at each of the n vertices of a regular n-sided polygon of side a lying in a plane.
(a) Show that the magnitude F_n of the net electrostatic force on any one of the corner charges can be written in the form Fn=a2kq2G(n), where G(n) is a dimensionless function depending only on n.
(b) Derive an explicit expression for G(n) in terms of elementary trigonometric functions of n.
(c) Keeping the perimeter P = na constant, evaluate n→∞limFn and interpret the physical meaning of your result.