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Statement of a problem № 3983

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Consider a rectangular waveguide of dimensions x = a and y = b, the wave travelling along the z-direction, the axis of the guide. Given that the z-component Hz satisfies the equation (d2/dx2+d2/dy2)Hz=(k^2-w^2ne)Hz (a) obtain the solution for Hz . (b) Obtain the cut-off frequency. (c) What are the similarities and differences between TMmn mode and TEmn mode?

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

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