Physics GRE Discussion Forums

Here's a link to the problem: http://grephysics.net/ans/0177/8

When there is a positive charge Q above an infinite grounded conducting plane, the method of images says the field is like that of the positive charge Q and negative charge -Q on the the opposite side of the plane. The problem here asks what the the total charge induced on the plane is, and the answer is -Q.

Can someone help me understand this? It isn't obvious to me why the charge distribution on the plane must have a total charge of -Q to produce a field above it that is as if there were a negative point charge -Q below it.

Thanks for the help!

Every electric field line coming out of the charge +Q terminates in the conducting plane (to convince yourself of this, think about what the dipole field created by a charge +Q and a charge -Q looks like). Apply Gauss's law: there is some electric flux coming out of the charge, which is proportional to Q. The same flux goes into the plane, so the plane has the same charge (but opposite, since the flux points into the plane).