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Justify. Rectangular waveguides do not support TEM wave.
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Solution:

Rectangular waveguides do not support TEM waves. wave having no axial component of $\vec{E}$ or $\vec{H}$ - If we assume the TEM wave exists within a hallow guide of any shape, the line of $\vec{H}$ will be a closed loop in a plane perpendicular to the axis $(\nabla, \bar{H})=0$

Now according to Maxwell eq,

$ \oint_L \vec{H} \cdot d \vec{L}=\int_3 \vec{J} \cdot d \vec{s}+\int_s \partial \bar{D} / \partial t \cdot d \vec{s} $

$\because$ the conductor is hollow having no inner conductor the axial current is displacement current. (Conduction current is zero.).

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