Rectangular Waveguide with obstacle

I have a rectangular waveguide with the dimensions and alignment shown below in the figure. At z = 0 there is an obstacle in the form of an infinitesimally thin perfectly conducting plate placed as shown in the figure. A TE10 mode wave traveling along +z direction is incident upon the obstacle. I want to obtain the resulting fields due to the presence of this obstacle. Are new modes created due to this obstacle? How does it effect the power flow thru the waveguide? How do I apply the boundary conditions?
Please suggest how to approach this problem.

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