Question
Show that TM modes can be characterized only by the electric scalar potential $\psi^c(x, y)$.
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## Showing TM Modes Can Be Characterized by Electric Scalar Potential $\psi^c(x,y)$ Show more…
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Show, from equations (8.1) and (8.2), that the magnetic field in the plane-polarized electromagnetic wave of Problem $9.3$ has components in both $x$ - and $y$ -directions. [When an electromagnetic wave propagating in a waveguide has only transverse electric field vectors and no electric field in the direction of propagation it is called a transverse electric (TE) wave. Similarly a transverse magnetic (TM) wave may exist. The plane-polarized wave of Problem $9.3$ is a transverse electric wave; the corresponding transverse magnetic wave would have $H_{z}, E_{x}$ and $E_{y}$ components. The values of $n$ in Problem $9.3$ satisfying the boundary conditions are written as subscripts to define the exact mode of propagation, e.g. $T E_{10}$.]
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