The instantaneous electric field inside a conducting rectangular pipe (waveguide) of width a is given by where βz is the waveguide’s phase constant. Assuming there are no sources within the...

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The instantaneous electric field inside a conducting rectangular pipe (waveguide) of width a is given by

where βz is the waveguide’s phase constant. Assuming there are no sources within the free-space-filled pipe determine the:

(a) Corresponding instantaneous magnetic field components inside the conducting pipe.

(b) Phase constant βz . The height of the waveguide is b.

Answered 142 days After May 07, 2022

Solution

Baljit answered on Sep 26 2022

57 Votes

a.
Given
E =y E0 sin(πx/a) cos(ωt-βzz)
E =Re[y E0 sin(πx/a) ej(ωt-βzz)]
E =Re[Eejωt]
here E=y E0 sin(πx/a) e-jβzZ
Now we know that magnetic field H is related to electric field E by following Relation
H= ∇ X E
So
H=x - z
H=x - z
H=-x E0 sin(πx/a) e-jβzZ +z (π/a)cos(πx/a) e-jβzZ
Now...

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The instantaneous electric field inside a conducting rectangular pipe (waveguide) of width a is given by where βz is the waveguide’s phase constant. Assuming there are no sources within the...

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