5. Two metal plates having and area A and separation d form a parallel plate capacitor....

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5. Two metal plates having and area A and separation d form a parallel plate capacitor. Take the area to be a square of length LVA with L» d. Let the vertical direction be the z axis and the horizontal direction the ax axis. The potential at the top z = d is held at a potential Vo, and that at the bottom is grounded (its potential is 0. (a) Use Laplace's equation to determine the potential in the region between the plates. (b) Determine E. (c) Determine the charge distribution on each plate. (d) Determine the capacitance of the parallel-plate capacitor. 5. Two metal plates having and area A and separation d form a parallel plate capacitor. Take the area to be a square of length LVA with L» d. Let the vertical direction be the z axis and the horizontal direction the ax axis. The potential at the top z = d is held at a potential Vo, and that at the bottom is grounded (its potential is 0. (a) Use Laplace's equation to determine the potential in the region between the plates. (b) Determine E. (c) Determine the charge distribution on each plate. (d) Determine the capacitance of the parallel-plate capacitor.