This is a question in my book: A point charge q is rotated 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? The answer in my book says that regardless of whether Q is at the center of the circle work done will always be zero.

Now I can understand why work done is zero when Q is at the centre, since the circle will be an equipotential surface for charge Q, field of Q always being perpendicular to displacement of q at each instant. But why is work done still zero even when Q is not located at the centre of the circle but somewhere else?

Electric fields are conservative fields.

The work done around any closed loop will always be zero.

That's because the work done when you move a unit charge between two points is equal to the potential difference between the points. But if you return to your starting point the potential difference must be zero.

@JohnRennie thank you!