Force on a conducting plate from reflected TE₁₀ mode in a waveguide

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Hogarth4
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Homework Statement



A TE_10 mode is propagating in a rectangular waveguide along the z-axis. If the waveguide is terminated with a perfectly conducting metal plate normal to the z-axis, then 100% of the electromagnetic radiation propagating in the guide will be reflected by the metal plate. If the dimensions of the guide are a by b with the cutoff frequency ω_c = cπ/a,

1) what is the force felt by the metal plate due to the reflected radiation?
2) if instead of a metal plate, a resistive plate which absorbed 100% of the incident radiation were used, what would be the force experienced by this resistive plate?

Homework Equations



F = q(E + v x B) ??



The Attempt at a Solution



For TE_10, B_z = B_o*cos(πx/a)??
 

Discussion

1) The force felt by the metal plate would be equal to the force exerted by the electric and magnetic fields of the incident radiation. Using the equation F = q(E + v x B), where q is the charge of the particle, E is the electric field, v is the velocity of the particle and B is the magnetic field, the force felt by the metal plate can be calculated. 2) If the waveguide is terminated with a resistive plate, then the force experienced by this plate will depend on how much of the incident radiation is absorbed by the plate. For example, if 100% of the incident radiation is absorbed, then the force experienced by the plate will be equal to the force experienced by the metal plate in the first case.