# Induced charge on a grounded conductor

say there is an infinite grounded conducting plane and a point charge of charge q is above it. the induced charge on the plane is -q and i know how to find this using the method of images to find the potential and then finding and integrating the charge density, but my text says that it should be intuitively clear that this induced charge must be -q. i'm just not seeing why it has to be, can anyone give me a simple explanation?

thanks.

StatusX
Homework Helper
Apply Gauss's law to a box that contains the entire region with z<=0 (strictly speaking, you should take the limit as the box gets infinitely large). Since the field at the box surface is the same in the case of the grounded conducting plane and the image charge, the total enclosed charges are the same in both cases.

how do you know that the field at the box surface is the same for the plane and the image charge? in the point charge case the field at z=0 is 2q^2/(4*pi*e*r^2) but i don't see how you know what the field is in the case of the plane.

StatusX
Homework Helper
Put the top side of the box above the plane.

My comment may be late, i register just now.