EAD234B_Homework5__2010

EAD234B_Homework5__2010 - EAD 234B: E&M Homework #5 Due...

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EAD 234B: E&M Homework #5 Due Thursday, May 13, 2010 (1) Consider the long wire shown below. (a) Find the potentials and the fields produced by a current I(t) = I 0 Θ (t) that turns on abruptly at t = 0 in a neutral, filamentary wire coincident with the entire z-axis. (b) Show that the electric and magnetic fields approach their expected values as t . (2) Consider a dipole d G , rotating in a plane (say, the x-y plane) with a constant angular velocity ω . (a) Find the angular distribution of the radiation. (b) Find the time-averaged total radiation. (c) Determine the polarization of the radiation wave. (3) Consider the current density located at the origin () ( ) ()() ˆˆ jt Jx j y x y y e ω αβ δ δ δ where α and β are real constants and 1 j = . a) Find the far-field Poynting vector. b) Find the value of β and α that makes the radiation pattern as nearly isotropic as possible. (4) Consider the case of a symmetrical, thin, center-fed antenna of length L as shown in the figure below. (a) Derive expressions valid in the far-field for E and H
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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_Homework5__2010 - EAD 234B: E&M Homework #5 Due...

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