EAD234B_Homework1_2010 - EAD 234B: E&M Homework #1 Due...

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EAD 234B: E&M Homework #1 Due Thursday, April 8, 2010 (1) The electric and magnetic fields at t = 0 are ( )( ) 0 ˆˆ , Ef z xBB f z y == G G with () 2 exp f za z =− a bell-shape function. (a) Find the electromagnetic energy and momentum density and their ratio. (b) Show that at t > 0 there are two wave-packets travelling in the directions ˆ z and ˆ z . (c) At what ratio 00 / E B α = is there is just one wave-packet? How much of the initial energy of the field is carried in the ˆ z and ˆ z directions? (2) Derive the dispersion relation for the ordinary mode ( ) , EBk B & ±± ± in a cold plasma (KT e = 0) where the effects of collisions are accounted for through a constant collision frequency v . You may assume the ions are sufficiently massive that they are fixed and thus only need treat the electron motion. Assuming real frequency ω , show that the index of refraction n = c/v ph and the wave number are now complex. Find expressions for the attenuation length δ = [Im( k )] -1 in the three limits (a) low frequency v< < p , and (c) high frequency > p
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This note was uploaded on 05/14/2010 for the course EAD 234 taught by Professor Ncl during the Spring '10 term at École Normale Supérieure.

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EAD234B_Homework1_2010 - EAD 234B: E&amp;M Homework #1 Due...

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