# the method of images and bringing a charge to an infinite grounded plane

The classic image problem is that of a point charge $$q$$ held a distance $$d$$ above a grounded plane. The solution is this problem is to replace grounded plane by a charge $$-q$$ a distance $$d$$ below the plane, see the figure (taken from Wikipedia)

With this substitution it is then straightforward to work out that the force of attraction between the charge $$q$$ and the plane is $$\frac{q^2}{ 4 \pi \epsilon_0 (2d)^2}.$$

If you release the charge $$q$$, the force acting upon it causes it to accelerate towards the plate, the force varying as $$1/d^{2}$$. Presumably, this energy gained by the charge comes from the work done keeping the plate grounded. It is obviously not an electro$$static$$ problem any more and em radiation will also be called into play. But, whatever, you can't physically supply an infinite amount of energy, so what eventually happens?