Lecture 43 : Rectangular Wave Guide and Transverse Magnetic Mode
Boundary conditions for the longitudinal electric field component
The component is parallel to all the four walls of the waveguide. Since the tangential field of the electric field is zero at the conducting boundary, we get the boundary condition for .
---------- (6.48)
The boundary conditions for = and = walls give = 0, = 0 and the boundary conditions for , and give
---------- (6.49)
---------- (6.50)
where and are integers.
Substituting for and , we finally get the solution for as
---------- (6.51)
Constant is essentially a combination of , , which gives the amplitude of the longitudinal component of the electric field.
component is parallel to all the four walls of the waveguide. Since the tangential field of the electric field is zero at the conducting boundary, we get the boundary condition for 
and 
, we finally get the solution for 
is essentially a combination of 
, 
, 
which gives the amplitude of the longitudinal component of the electric field. 
