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## Homework Statement

Having trouble understanding why it is that inside a waveguide sides x=a,y=b propagating in z, subject to b.c. E parallel= 0 and Bperp=0... that for TE Bz=Bcos(pinx/a)cos(pimy/b) but for TM Ez=Esin(pinx/a)sin(pimy/a)?

## Homework Equations

E parallel= 0 and Bperp=0

For TM Bz=0 for TE Ez=0

for TM Bz is proportional to d/dx(Bz)

^ hence the cosine solutions

## The Attempt at a Solution

Why is it that inside a waveguide sides x=a,y=b propagating in z where E parallel= 0 and Bperp=0 is it that Bz=Bcos(pinx/a)cos(pimy/b) but Ez=Esin(pinx/a)sin(pimy/a)?

I know it is because bz is proportional to d/dx(bz) so we get the cosine derivative to sine and we fit our b.c. there but ez is also proportional to d/dx(ez) however we see that Ez has a sine dependence not cosine dependence..