Opt2 - used to connect it to two perfectly conducting...

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PHY 505 Classical Electrodynamics I Fall 2010 Optional problems Set 2 (no submission, no grading) Problem O.7. Solve the problem shown in Fig. 2.19 of the lecture notes (reproduced on the right), in particular, find the distribution of the electrostatic potential at the cylinder’s axis. Problem O.8. A fixed dipole is placed in the center of a spherical cavity of radius R carved inside a uniform, linear dielectric. Find the electric field distribution in the system (both for r < R and r > R ). Hint : Start with the assumption that the field at r > R has a distribution typical for a dipole (but be ready for surprises :-). Problem O.9. A long, round cylinder is made of a ferroelectric material with fixed, constant polarization P perpendicular to cylinder’s axis. Calculate the distribution of electric field both inside and outside the cylinder. Problem O.10 . Calculate resistance of a thin, uniform, conducting foil of thickness t , cut into the shape of a ring, with a narrow cut
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Unformatted text preview: used to connect it to two perfectly conducting electrodes (see Fig. on the right), for an arbitrary ratio b / a . Problem O.11 . Calculate (self-)inductance of a toroidal solenoid with the cross-section shown in Fig. on the right ( r ~ R ), filled with a material of magnetic permeability , with N >> 1 wire turns uniformly distributed along the perimeter. Check your results by analyzing the limit r << R . Hint : You may like to use the following table integral MA (6.11): . 1 for , 1 1 1 ln 1 2 2 2 a a a d a a Problem 0.12 . A planar, uniform superconducting film of thickness t ~ L carries a finite supercurrent J per unit width. Use the London equation to find the current distribution over the film thickness. a b ? V I t I R r z 2 / V 2 / V 2 / V z h t...
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