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  • Calculate the potential energy of a point charge -q placed along the axis due to charge +Q uniformly distributed along a ring of radius R.

Calculate the potential energy of a point charge -q placed along the axis due to charge +Q uniformly distributed along a ring of radius R. Sketch PE as a function of axial distance z from the center of the ring. Looking at the graph, can you see what would happen if -q is displaced slightly from the center of the ring?

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Explanation:-

The potential energy of a point charge q is U and this point is placed at potential V, U=qV

A negatively charged particle is placed at the axis of the ring with charge Q

Let a be the radius of the ring

The electric potential at the axial distance is given as

V=\frac{1}{4\pi \epsilon _{0}}\frac{Q}{\sqrt{z^{2}+a^{2}}}

The potential energy, U is given as

U=\frac{1}{4\pi \epsilon _{0}}\frac{Qq}{\sqrt{1+\left ( \frac{z}{a} \right )^{2}}}

When z=infinity, U=0.

When z=0, U is given as

U=\frac{1}{4\pi \epsilon _{0}}\frac{Qq}{a}

 

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