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

Question

Philoid · Accepted Answer

• The potential energy (U) placed at potential V,

• In our case a negative charge particle is placed at the axis of a ring having charge Q

• let the ring has radius r, the electric potential at an axial distance d from the centre of the ring is

• hence potential energy of a point -q is

⇒

At d = 0

At d = ∞ U → 0

the variation of potential energy with d is shown in fig

the charge -q displaced would perform oscillation nothing can be concluded just by looking at the graph