A cube with side length 10 Angstroms has electrons affixed at each corner. To be clear, each corner has just one electron and the center of the cube is at the origin of the coor- dinate system. The top and bottom faces of the cube are parallel to the xy-plane and the z-axis intersects the center of the top and bottom faces of the cube. 1. Draw a diagram of this configuration with a coordinate system and be sure to label each charge and the origin. 2. Calculate the electrostatic potential energy due to the charges only at the corners in the xy-plane (z = 0) for the portion of the plane within the cube. Assume that there is a proton as a test charge at the center of the cube. Make a surface plot of this potential energy in units of electron volts. 3. Do the same but now assuming that there is an electron as a test charge at the center of the cube.