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problem_3

# problem_3 - assume nonrelativistic motion[continued on back...

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ASTRONOMY 822 Electromagnetic Radiation Problem Set 3 due Wednesday, October 19 at class time 1) A particle of charge q is moving at a constant speed v q along a straight line. You are located so that the particle’s distance at closest approach is b (see the Fgure below). Let t = 0 be the instant when the particle is at its closest approach. a) What is ~ E at your position at t = 0? What is ~ E at your position in the limit t À b/c ? b) What is ~ B at your position at t = 0? What is ~ B at your position in the limit t À b/c ? 2) Suppose that a particle of charge q is oscillating along the z axis, such that ~ r q ( t ) = ˆ e z z 0 cos( ωt ) . a) What is the power emitted per unit solid angle, dP/d Ω, in a direction at angle θ to the z axis? b) What is the polarization of the emitted radiation at θ = 0? What is the polarization of the emitted radiation at θ = π/ 2? (Hint: This problem was inspired by problem 3.2 in the textbook. You may

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Unformatted text preview: assume nonrelativistic motion.) [continued on back] 3) Consider an electric dipole consisting of a charge-q and a charge + q separated by a constant distance D . a) If the dipole is stationary, what is ~ E ( ~ r ), where ~ r is measured from the point midway between the charges? What is ~ E in the limit that r → ∞ ? b) Suppose that the dipole is rotating about the point midway between the charges, with angular frequency ω (see Fgure). What is ~ E ( ~ r, t )? What is ~ B ( ~ r, t )? What is the power emitted per unit angle, dP/d Ω, in a direction at angle θ to the axis of rotation? (Hint: Problem 3.2 of the textbook might be useful for this problem, too. You may assume nonrelativistic motion.)...
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problem_3 - assume nonrelativistic motion[continued on back...

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