Does inducing charge on a grounded conductor do work?

Question

Imagine a grounded conductor as an plane of infinite area. If I bring a charge to a close proximity to the plane, it induces some charge distribution on the conductor.

The question is: is any work being done on the (induced) charge during this process?

RE60K · Answer

Yes, By taking an electrical image of the charge wrt plane you can understand that the magnitude of work will be:
$$ |W| = frac 1{4piepsilon_0}frac {q^2}2 left|frac1y-frac1dright|$$
where we carry a charge q from distance d to distance y from earthed conducting plane.

Alfred Centauri · Answer

is any work being done on the (induced) charge during this process?

Clearly, the potential energy of the induced charge is unchanged since the conductor is an equipotential surface.

The induced charge is, I assume, static so the kinetic energy of the induced charge is unchanged.

If work has been done on the induced charge, in what form is the energy stored?

Does inducing charge on a grounded conductor do work?

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