A ring of radius a, total charge +Q lies in the xy-plane, centred on the origin

Question

A ring of radius a, total charge +Q lies in the xy-plane, centred on the origin (see Fig. ). A point charge +qo lies a distance z above the centre of the ring, and experiences a force given by: (F=(qQ/4pixia^2)sin hetacos^2 hetaz) %u0302 Determine the electric potential energy of the point charge at this position. If the ring was replaced by a solid disc (radius a, surface charge density +%u03C3), the point charge would have an electric potential energy given by: (U=qsigma/2xi(sqrt(z^2+a^2)-z)) Determine the electric force experienced by the point charge +qo at a distance zabove the disc.

Explanation / Answer

Potential V(z) due to the ring = kQ / sq rt [z^2 + R^2]
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Electric Field on the axis of the ring =E =kQz / [z^2+R^2]^(3/2)
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