PHYS 685: Classical Electrodynamics I
Spring 2021
Home assignment ] 6
Due 4:30 pm, April 7, 2021
Problem 1 [20 points]
Consider a uniformly charged ring of radius R and total charge q. A grounded conducting sphere of radius Rs < R is placed at the center of the ring (see figure below).
Calculate: (a) the potential everywhere outside the sphere (r > Rs ), (b) the induced
charge density on the surface of the sphere, (c) the total induced charge on the surface
of the sphere, (d) the interaction energy between the ring and the sphere, and (e) the
force acting on the ring per unit length. Solve the problem by two methods:
1. [10 points] The image charge method.
2. [10 points] The Green’s function method.
3. [5 extra credit points] Using the solutions you obtained and your favorite computer
program, create contour plots showing the equipotential surfaces everywhere outside the sphere for Rs /R = 0.1, Rs /R = 0.3, and Rs /R = 0.8.
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