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 \(W = \vec F \cdot \overrightarrow {dx} \)  and force \(\vec F = Q \cdot \vec E\) 

\( \Rightarrow W = Q \cdot \vec E \cdot \overrightarrow {dx} \)

As displacement vector is perpendicular to Electric field

∴  \(\vec E \bot \overrightarrow {dx} \) 

So that dot product of \(\vec E\) and  \(\overrightarrow {dx}\) is

 \(\vec E \cdot \overrightarrow {dx} = \vec E \cdot \overrightarrow {dx} \cos \theta \) 

Where θ = 90°

\(\therefore \vec E \cdot \overrightarrow {dx} = \vec E\overrightarrow {dx} \cos 90^\circ = 0\)

Hence work done is zero at all points.