 # a) A point charge q is positioned in front of two semi-infinite gro...

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a) A point charge q is positioned in front of two semi-infinite grounded conducting planes that meet at right angles, as shown in the diagram below. What is the force on the charge q? y 2d 9 d X b) A wire loop, with rectangular segments in the xy and x2 planes, is carrying a steady current I, as shown in the digram below. The lengths of the sides of the loop are a and 2a as indicated in the diagram. What is the resulting magnetic field B at distances r far from the center of the loop, i.e. T >> a? Z 2a a a a I 2a y a x c) Consider a very long straight wire of length L and radius a carrying a uniform steady current I. If the wire has a uniform resistance per unit length, R/L, then there will be a voltage drop down the length of the wire, V = IR, and hence an electric field in the wire, E = V/L. Find the rate of electromagnetic energy flowing through the surface of the wire. (Assume that L is SO long that you may ignore the effects at the ends of the wire.) Does energy flow into or out of the wire? You answer should look familiar. Give a physical explanation for your result. d) In Problem Set 7 you derived the Faraday effect. According to this effect a linearly polarized electromagnetic wave, traveling through a dielectric in the presence of a uniform magnetic field B, has the direction of polarization rotated as it passes through the material. A naive application of the principle of superposition might argue against the existence of such an effect: if a linearly polarized wave with fixed direction of polarization, and uniform B = 0, is one solution to Maxwell's equations, and a uniform B # 0 and no wave is another solution, then the sum of these two solutions should itself be a solution; hence the presence of the uniform B # 0 should have no effect on the propagation of the wave! What is wrong with this naive argument?

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