What is the Total Induced Charge on a Grounded Conducting Plane?

[dudu1]

A positive charge Q is located at a distance L
above an infinite grounded conducting plane.
What is the total charge induced on the plane?
(A) 2Q
(B) Q
(C) 0
(D) -Q
(E) -2Q

I know the answer is C, but why? Thanks a lot!

 

[jonspalding]

The answer is D. The induced charge is equal and opposite to the charge q.

I refer you to pg. 123 of Griffith's "Introduction to Electrodynamics" for a derivation.

But by intuition alone, it wouldn't make sense for the induced surface charge to be zero; the presence of the charge q will tend to push positive charge (or the opposite, attract negative charge) to the surface closest to it. This causes an "image charge" to be produced within the conducting plane. The force experienced by the charge q is equal to that of a charge -q located a distance L beyond the surface of the plane; i.e. the force will be -q*q/(2L)^2 (I have dropped the constants that show up in Coulomb's law).