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EAD 234A: E&M Homework #3 Due Thursday, January 28, 2010 1. Use the method of images to find the Green’s function of the system shown in the figure below. (The bulge on the conducting plane has the shape of a semi-sphere of radius R .) 2. Find the 2D Green’s function in: (i) infinite free space, and (ii) free space above a conducting plane. Use the latter result to calculate the distribution of the electric potential created by the 2D system shown in figure below. (The gaps between the conducting fragments are negligibly small.) Hint : Physically, the 2D Green’s function may be viewed as the electrostatic potential created by a thin, straight, infinitely long wire, with the uniform charge density 0 4 λ πε = . 3. A point dipole of dipole moment p is placed a distance L from the center of a grounded conducting sphere of radius R. For simplicity, assume that the dipole points away from the center of the sphere. (a) Use the method of images to find the potential in the region exterior to the sphere.

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