Problem.Set.4

# Problem.Set.4 - instantaneous form, u x ,0 f x exp ik x...

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Problem Set 4: (Assignment 5) For a given system the electric field and current density are given by Assignment 5 E r , t E 0 exp z ct 2 2 L 2 cos k 0 z ct  e 1 J r, t J 0 exp z ct 2 2 L 2 cos k 0 z ct 0 e 1 (a) Calculate the magnetic flux density, B r , t . (b) Calculate the frequency dependent fields and current densities e r , , b r , ,and j r , . (c) What are the units of these three quantities in the gaussian units used by Jackson , in the SI (MKSC) units? (d) Starting with the results of part (b) evaluate e r , b r ,and j r defined in the notes. (e) Let 0 /6 and k 0 L 2 10 12 and calculate the time average of E r , t   J r , t over the period from t T /2 to t  T /2 at z  L and at z 0. (Note, a tabulated integral). (f) Plot the results of part (e) for 0 cT / L 1. ( Assignment 6A) Jackson Problem 7.19 - An approximately monochromatic plane wave packet in one dimension has the
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Unformatted text preview: instantaneous form, u x ,0 f x exp ik x with f x the modulation envelope. 1 f x N 1 exp | x | 2 2 f x N 2 exp 2 x 2 4 3 f x N 3 1 | x | 1 2 x 2 4 f x N 4 1 2 x 2 (a) Calculate the wave number spectrum | A k | 2 for each of the above forms for f x . (b) Explicitly evaluate the rms deviations from the mean, x and k . (c) Using graphs compare the functions | f x | 2 and the functions | A k | 2 ....
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## This note was uploaded on 12/19/2010 for the course PHYS 423 taught by Professor G. during the Spring '10 term at Missouri S&T.

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