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Unformatted text preview: Problem set 4 1. Jackson 4.1. 2. Show that a charged particle in a good quantum state of angular momentum l, m has no permanent electric dipole moment. 3. An infinitely long copper cylinder of radius a is surrounded by a cylindrical shell of inner radius a , outer radius b . The dielectric has a dielectric constant . The combined cylinder is now placed in a uniform static electric field E o perpendicular to the axis of the cylinder. (a). Before solving this problem, find all the z-independent solutions of Laplaces equation in cylindrical coordinates. (b). State the boundary conditions at r = a , r = b and as r (c). Using the solutions of Laplaces equation found in part (a), find the electrostatic potential in the three regions r < a , a < r < b and r > b (d). Find the charge per unit area on the surface of the metal cylinder as a function of . 4. Jackson problem 4.5 (part a only)....
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