A thin insulating ring of radius carries a charge spread uniformly around it
PHYSICS · Multi-part · Fermi University Physics · Electricity, Magnetism & Electromagnetism · Electrostatic fields and potential · Electrostatic fields and potential
Electricity, Magnetism and Electromagnetism, Ch Electrostatic potential, potential energy and the energy of the field
Problem
A thin insulating ring of radius a=0.12m carries a charge Q=+4.0nC spread uniformly around it. The ring lies in the xy-plane with its centre at the origin, so its axis is the z-axis. All the charge is at rest and V=0 at infinity. Take P to be the point on the axis at z=0.16m.
((a)) Every element of the ring is the same distance from P. Use this to write the potential V(z) at a general axial point and evaluate it at P.
((b)) By differentiating your V(z), find the field component Ez at P and state its direction. (On the axis Ex=Ey=0 by symmetry, so this is the whole field there.)
((c)) Find the electric field energy density at P, and hence the field energy stored in a cube of side 1.0mm centred on P, over which the field may be treated as uniform.