A point charge q is rotating along a circle in the electric field generated by another point charge Q. The work done by the electric field on the rotating charge in one complete revolution is:

Concept:

• Electric field is the force acting on a charge by another charge i.e. force per unit charge.
• Electric work done is the work done on a charged particle by an electric field.

Explanation:

Given that:

A point charge (Q) is rotating along a circle in the electric field generated by another point charge P.

• Electric field due to point charge is spherical or it is outside the given circle.
• A charge is moving along the circle, so it displacement vector is always perpendicular to the electric field vector.

Now, work done   and force  

As displacement vector is perpendicular to Electric field

∴   

So that dot product of  and   is

Where θ = 90°

Hence work done is zero at all points.