Force felt by plates in a waveguide

[Hogarth4]

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)??

 

[member 553083]

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.