Consider the following configuration: A point charge sits in the upper right $(x>0,y>0,z)$ space. The other quadrants are separated by two conducting planes in the $(x=0,y,z)$ & $(x,y=0,z)$ plane. I want to calculate the work needed to create said configuration.
The electric field can be calculated using three image charges, one sitting in each quadrant.
For the work I first consider the simpler problem of bringing a charge towards a single conducting plane and find out: The work needed is simply half the work needed to bring the charge towards a real one. This can be explained (so does Griffith e.g.) by noting that in the mirror configuration, we only have a non-vanishing field in one half of the space (where both parts are symmetric) and the work needed is simply the energy stored in the field.
But now, when extended to my problem, things get inconsistent. For each image charge I need half of the work required (compared to the case with real charges), thus the total work will be half. But intuitively I would think (extending the previous argument) that the total work (the energy stored in the configuration) is a quarter (since the field is only non-vanishing in a quarter of the space).
What am I missing?
