Answer Happy

Problem 13.2. Method of images = 2 Two grounded semi-infinite vertical conducting planes meet at right angles along the z axis. One plane extends along the positive x axis (so that it forms the x > 0 half of the x-z plane). The other runs along z the positive y axis (so that it forms the y20 half of the y-z plane). A point charge q lies in the x-y plane at the point x = V3 a, y=,z=0. A student has proposed that the electrostatic potential in the region containing the charge q and bounded by the planes can be found by using three image charges also placed in the x-y plane: -q at x = V3 13 V3 a, y=-a, -q at x = a, and +9 at x = - y=- 9 1 2 a, y = a, 2 2. 2 a. a) Draw a large clear picture of the x-y plane. In this picture, indicate the portion of the axes along which the grounded planes run, the position of the original charge, and the positions and charges of the three image charges. b) Write the electrostatic potential do (x, y, z) due to the original charge in rectangular coordinates. c) Write the electrostatic potential Oimage (x, y, z) due to the three image charges. d) Write down the total potential Q = ♡o + Mimage due to the original charge and the three image charges. Show that this potential is zero at the positions of the grounded conducting planes. Is the student's proposal that the potential in the region containing the charge q and bounded by the planes is given by this image-charge configuration correct?