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# Opt1 - the lecture notes and its application to the problem...

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PHY 505 Classical Electrodynamics I Fall 2010 Optional Problems Set 1 (no submission, no grading) Problem O.1. Two thin, straight parallel filaments, separated by distance d , carry equal and opposite uniformly distributed charges with linear density - see Fig. on the right. Find the electrostatic force (per unit length) of the Coulomb interaction between the wires. Compare the result with the Coulomb law for the force between the point charges, and interpret their difference. Problem O.2. Can one create the electrostatic fields presented below by sets of their components in Cartesian coordinates { x , y , z }, in a finite region of space? (i) { yz , xz , xy } (ii) { xy , xy , yz } Problem O.3. Calculate the force (per unit area) exerted on a conducting surface by an external electric field. Compare the result with the definition of the electric field given by Eq. (1.6) of the lecture notes, and comment. Problem O.4. Read (and understand :-) the discussion of the Schwarz-Christoffel integral in Sec. 2.4 of
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Unformatted text preview: the lecture notes, and its application to the problem shown in Fig. 2.10. Complete the problem’s solution by calculating the distribution of the surface charge of the conducting semi-planes. Can you calculate the mutual capacitance of the planes (per unit length)? Problem O.5 . Calculate the potential energy of a point charge placed in the center of a spherical cavity which was cut inside a grounded conductor. Problem O.6 . A conducting plane located at z = 0 is separated into two parts with a very narrow, straight cut along axis y , and voltage V is fixed between the resulting half-planes, as shown in Fig. below. Use the Green’s function method to find the distribution of the electrostatic potential in all the space, and the electric field on the symmetry plane ( x = 0). Looking at the result, could be the problem solved in a simpler way? d x z 2 / V 2 / V...
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