How do I get the boundary conditions of the parallel plate waveguide?

In the book Microwave Engineering,when the author calculate the TM modes of the parallel plate waveguide,the boundary conditions is that ez(x, y)=0 when y=0,d; and in TE modes,Ex=0 when y=0,d; and d/dx = 0; Why?

Because a perfect conductor (assumed in the derivation of the mode patterns) cannot support an electric field. Therefore the electrical field components tangential to the conductors are necessarily zero, as in the cases of the TE & TM modes.

I know this post is old, but I would like to know if the magnetic field is also zero at the boundaries?