## Wave guides

blackcat007
Posts: 378
Joined: Wed Mar 26, 2008 9:14 am

### Wave guides

In Griffith's Electrodynamics he states: for a wave guide, considering the walls as perfect conductors we have Et=0 and Bn=0 at the inner walls (considering E and B to be 0 inside the material) Et= is the transverse electric field and Bn is the normal magnetic field.

the first case Et=0 is understandable from the reflection at a conductor, where E_0R=-E_0I and E_0T=0 thus Et=0
also Bn=0 since inside the material B=0
but En is not 0 since there can be free surface charges, which is also conceivable but for the case of Bt we consider it as non 0 since there can be a free surface current. But just few pages earlier, when Griffith just introduced the reflection at a conducting surface, he said that for an ohmic conductor, J=(sigma)E thus surface current is 0 since it would take infinite electric field.
Then why don't we use this same consideration in the case of waveguides? are we using non-ohmic conductors?

sravanskarri
Posts: 58
Joined: Sat Jun 14, 2008 10:19 pm

### Re: Wave guides

Yes the 4 th boundary condition is indeed a confusing .

Kf can be zero at the boundary between two non-ohmic conductors/ non conducting -conductor where he is trying to draw an analogue to the boundary condtions between two di-electrics, a case he considered earlier.I think Kf =0 follows from the fact that it requires an infinite charge build up along the conductor in order to have a free current and hence an Infinite electric field. However I could not convince myself fully as we are considering time varying electro magnetic fields here and not sure if the transient surface currents will ultimately decay to zero. However the following equations seem to support to my argument.

For conductors:

d( rho_free(t))/dt = -(sigma)/epsilon ( rho_free(t))
sigma -> conductivity
rho_free -> free surface charges

solving this rho_free (t) = exp ( -sigma/epsilon).rho_free(0)
rho_free -> 0 as sigma -> Infy and hence d( rho_free(t))/dt -> 0.

For wave guide, the same idea can be applied to get the wave eqns and Boundary conditions.So, to conclude, Waveguides here being ( hollow perfect conductors ) are in fact a better fit than the ohmic conductors for Kf =0 in my opinion.Let me know what you think.