Question

Consider the region between two electrodes in a spherical capacitor, where the radius of the center electrode is a and the radius of the outer shell is ( < ). The central electrodes are held at a potential and the outer shell is grounded.

a. Use Laplace's equation to determine the electric potential (answer: = [()()][( (/))] in the region between the two electrodes in a spherical capacitor. As in the course, the solution from Laplace's equation in spherical coordinates to the form = (/) + . b. From your answer above, determine .

c. From your answer in b), determine the surface charge density and the total charge on the area at r = a. d. From what you know so far, determine the capacitance of this spherical capacitor?