Question

Transverse electric field components inside a rectangular waveguide for TEₘₙ mode is given below:

Eₓ = nA cos (mnx/a) sin (mnx/a) e⁻ʲᴮᶻ
Eᵧ = mB sin (mnx/a) cos (mnx/a) e⁻ʲᴮᶻ where A and B are constants.
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(i) What are the boundary conditions that should be satisfied by Eₓ and Eᵧ?

Answer 1

The boundary conditions for Eₓ and Eᵧ in a rectangular waveguide TEₘₙ mode are: Eₓ = 0 at the conductor walls and Eᵧ = Eₓ at the top and bottom surfaces.

Step-by-step explanation:

The boundary conditions that should be satisfied by Eₓ and Eᵧ in a rectangular waveguide for the TEₘₙ mode is:

1. At the conductor walls (x = 0 and x = a), the electric field components Eₓ and Eᵧ must be equal to zero.

2. At the top and bottom surfaces (y = 0 and y = b), the electric field components Eₓ and Eᵧ must satisfy the boundary condition of continuity, which means they must have the same value.

These boundary conditions ensure that the electric field components adhere to the geometry and constraints of the rectangular waveguide.