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Statement of a problem № 3982

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Consider a rectangular waveguide of dimensions x = a and y = b, the TMmn wave travelling in the z-direction which is the axis of the guide. Given that the z-component Ez satisfies the equation (dz/dxz+dy/dyz)Ez=(k^2-w^2ne)Ez obtain (a) the solution for Ez and (b) the cut-off frequency.

Solution:
Consider a rectangular waveguide of dimensions x  = a and y  = b, the TMmn  wave

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