A current distribution consists of N identical sources. The k^th source is identical to the first source except for a rigid translation by an amount R_k (k = 1, 2, . . . , N). The sources oscillate at the same frequency ω but have different phases δ_k. That is,

(a) Show that the angular distribution of radiated power can be written as the product of two factors: one is the angular distribution for N = 1; the other depends on Rk and δ_k but not the structure of the sources.
(b) The planes of two square loops (each with side length a) are centered on (and lie perpendicular to) the z-axis at z = ± a/2. The loop edges are parallel to the x and y coordinate axes. Find the angular distribution of power, dP/dΩ, in the x-z plane if the current at all points in both loops is I cos ωt. Make a polar plot of the angular distribution for ωc/a = 2π and ωc/ac (c) Repeat part (b) when the current in the upper loop is I cos ωt and the current in the lower loop is −I cos ωt.

Transcribed Image Text:

jk x exp[-i(wt + 8k)].