1) The first case we consider is a charge q placed a distance d along the z axis in front of an infinite flat grounded plane (=0 on the plane). We want V²= -4πq(x)(y)(z — d), and = 0 for z = 0. If we find a solution to the above problem, we know it is the unique solution. q 7=0 Solution: put a fictitious image charge -q at z = -d. The potential is then the Coulomb potential from the real charge +q and the image charge -q. ø(r) = q -9 √ x² + y² + (z − d)² - x²+y+2+(z+d)² (2.2.1) Discussion Question 2.2.2 Area A W q Z Consider a point charge q a distance d in front of a thin conducting plane of thickness w, as shown in the diagram. The plane has a fixed net charge Q on it. What is the electric field to the right of the plane, to the left of the plane, and inside the plane? What is the force between the charge q and the plane? Assume that the side area of the plane A is finite, so that the average surface charge Q/2A is finite, however you make work the problem ignoring edge effects, i.e. assuming the plane is effectively infinite.

1) The first case we consider is a charge q placed a distance d along the z axis in front of an infinite flat grounded plane (=0 on the plane). We want V²= -4πq(x)(y)(z — d), and = 0 for z = 0. If we find a solution to the above problem, we know it is the unique solution. q 7=0 Solution: put a fictitious image charge -q at z = -d. The potential is then the Coulomb potential from the real charge +q and the image charge -q. ø(r) = q -9 √ x² + y² + (z − d)² - x²+y+2+(z+d)² (2.2.1) Discussion Question 2.2.2 Area A W q Z Consider a point charge q a distance d in front of a thin conducting plane of thickness w, as shown in the diagram. The plane has a fixed net charge Q on it. What is the electric field to the right of the plane, to the left of the plane, and inside the plane? What is the force between the charge q and the plane? Assume that the side area of the plane A is finite, so that the average surface charge Q/2A is finite, however you make work the problem ignoring edge effects, i.e. assuming the plane is effectively infinite.