Parallel plate waveguide, step discontinuity

[EmilyRuck]

Hello!
You can find in the picture attached a parallel plate waveguide which has an a1 height before the step and an a2 height after the step. The plates are perfect conductors and the step is ideal.
I can't determine which physical quantities are continuous across this discontinuity.
Suppose that a TEM wave is travelling, with the showed Ex and Hy (outgoing from the screen). I'm sure the voltage is constant: if I connect DC power supply, the voltage V between the two plates is the same before and after the discontinuity. But the electric field?
If it was a condenser, we had

V = E*d

where d is the distance between the plates. So, if d changes, E changes too. But E must be continuous according to my notes !
What's wrong? The voltage cannot change!
Thank you anyway,

Emily

 

[Valerie Park]

In this case, the electric field is continuous. The voltage, defined as V = E*d, is not constant across the waveguide, because the distance (d) between the two plates changes from a1 to a2. However, the electric field (E) stays the same before and after the discontinuity. This is because the waveguide is made up of perfect conductors, so that the electric field is shielded from the step.