An electric field in free space is given in spherical coordinates as E s (r) E 0 (r)e jkr a V m (a) Find H s (r) assuming uniform plane wave behavior (b) Find S (c) Express the average outward power in watts through a closed spherical shell of radius r, centered at the origin (d) Establish the required functional form of E 0 (r) that will enable the power flow in part c to be independent of radius With this condition met, the given field becomes that of an isotropic radiator in a lossless medium (radiating equal power density in all directions)

Question: An electric field in free space is given in spherical coordinates as E s (r) = E 0 (r)e jkr a V/m. (a) Find

An electric field in free space is given in spherical coordinates as E_s (r) = E₀(r)e^−jkr a_θ V/m.

(a) Find H_s (r) assuming uniform plane wave behavior.

(b) Find < S >.

(d) Establish the required functional form of E₀(r) that will enable the power flow in part c to be independent of radius. With this condition met, the given field becomes that of an isotropic radiator in a lossless medium (radiating equal power density in all directions).

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