110224_hw6 - o and its width Δx. 3. Determine the Fourier...

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February 24, 2011 PHYS 4132 Homework 6 Due date: March 3, 2011 1. The electric field of an electromagnetic wave in vacuum is given by E = (0, 2π cos(7π ×10 8 t + 7/3π x ), 0), where E is in volts/meter, t in seconds and x in meters. Determine a. The frequency f, b. The wavelength λ, c. The direction of propagation of the wave, d. The direction of the magnetic field. Verify your results and understanding by using the tool at http://www.phys.lsu.edu/classes/spring2011/phys4132/hw/superposition.html . 2. The potentials of an electromagnetic wave packet are A = A(x – ct) e z , A(x) = - dk f(k) e ikx , φ=0. Consider the following cases a. f(k) = f 0 exp( - γ k 2 /2) b. f(k) = f 0 exp( - α |k|) c. f(k) = f 0 Θ(α - |k|) Draw the wave packet A(x -ct) as function of x and determine its center x
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Unformatted text preview: o and its width Δx. 3. Determine the Fourier series of a periodic square wave with period a . Verify your result by superimposing waves with the leading terms at http://www.phys.lsu.edu/classes/spring2011/phys4132/hw/superposition.html and attach a plot showing your result. 4. In three dimensions one can also have spherical waves, which diverge symmetrically from a point source (or converge toward a point). Describe spherical harmonic waves. a. write down the wave equation in relevant coordinates. b. find the solution to the wave equation. c. draw the real part of the solution as function of r and for two times t 1 = t and t 2 = t + τ/2....
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This note was uploaded on 06/07/2011 for the course PHYS 4132 taught by Professor Kutter during the Spring '11 term at University of Florida.

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