# Electric Charge Image Theory - Half-Infinite Planes

by aphid
Tags: charge, electric, halfinfinite, image, planes, theory
 P: 2 1. The problem statement, all variables and given/known data A point charge Q lies along the axis of symmetry between two half-infinite grounded conducting plates which form an angle theta (less than or equal to 90 degrees). a. What are the magnitudes and locations of the image charges? b. What is the total charge on the conducting plates? c. Where does the charge come from? 2. Relevant equations An application of Laplace's Equation I believe . . . 3. The attempt at a solution I'm at somewhat of a loss here. The image of a point charge situated above a single infinite plane is simply its negative mirror image, resulting in an equivalent voltage field above the plane. My intuition tells me that I can somehow use superposition of the infinite plane case, but it would be a shot in the dark. I'm also fairly certain that a total charge -Q accumulates on the conductor, but I don't know how to explain this. Any insight into this problem would be greatly appreciated.
 Sci Advisor PF Gold P: 2,015 Start with finding the image locations by geometric construction. The first image is just the usual one you are familiar with (times two). But there's an image of each image in its opposite sheet. And so on. You'll have an infinite series.
 P: 2 Not sure if I am doing this correctly (see attached image). Am I supposed to extend each plane, effectively creating two intersecting infinite planes? It gets pretty messy once I start projecting across the 'imaginary' portions of the planes. Attached Thumbnails