# very basic silly question about electromagnetic waves

Status
Not open for further replies.

#### NoHa111

##### Junior Member level 3
sorry,but i have this problem as an assignment>>it is very silly basic question about maxwell's equations but i don't know how to solve it
the question is:
use maxwell's equations to show that it is impossible for the TEM wave to exit with any single conductor wave guide (such as rectangular or circular wave guide)
HINT:for the integration over a closed loop of H.dl to have value in the transverse plane there must be alongitudinal flow of current (conductor or displacement)

note:in question it is written exit it may be exist i don't know!!!!!

Hi

You can refer ny book particular which gives proper xplanation of it.

regards
mstripman

the correct word is "exist". All you have to do is to assume a TEM mode and show that the boundary conditions are not met by the TEM mode.

### NoHa111

Points: 2
basically a tem wave does not have ez and hz. so it will not satisfy waveguide equations for a single conductor waveguide.

well my firend about ur question .u should at first know that it is not possible to have tem in rectangular n circular wave guides as they r hollow and no inside conductor on which any propagation of wave takes place so in order to compensate that inner conductor in rectangular /circular wave guides any other part of wave takes the direction of that conductor to fullfill the necessary condition of propagation. u can see these solutions in filelds n wave electromagnetics" by david cheng
or a good book which i have seen that sols myself
"foundations of microwave eng" by collin

If you rigorously want to derive this from Maxwell's equations, first assume that TEM propagation does exist. Then you can show that the transverse parts of the fields must satisfy Lapalace equation (in 2D, just like static fields) and hence should be writable in the form of gradient of a potential. This potential can only be zero (or a constant) in the interior of a single conductor waveguide because of the uniqueness theorem that applies to the solution of Laplace equation. Hence the transverse components must be zero, which proves that TEM is not possible.

-svarun

PS: I would love to hear about more intuitive proofs. I am working on one such and will post it when it is ready.

Hi all,
the following is not a proof, however, it shows what was asked in the question:

Consider a rectangular/circular waveguide (no inner conductor), cartesian coordinate system.
TEM mode is assumed and direction of propagation is the z-axis.

a. Maxwell: rot x H = jwεE

b. Choosing a surface cut in the transverse plane of the waveguide and integrating both sides of the above:
∫(rot x H)•ds = ∫(jwεE)•ds
c. Using Stokes' theorem (forming Ampere's law):
∫(H)•dl = ∫(jwεE)•ds

d. Following the TEM mode assumption: Ez=Hz=0, while Ex,Ey,Hx,Hy≠0.
ds=ds•1z
dl=a function of x and y unit vector.

e. Solving c using d zeros the right side whereas the left side ≠ 0.

Hence, TEM mode cannot exist without an inner conductor that satisfies Ampere's law.

Regards,
P.

Can you please let me know where you have used the fact that, there is only one conductor and not two conductors ?

-svarun

I hope the file attached clarifies this.

I can rephrase the assumption and say: "Think of a single conductor with nothing inside, as shown in the PDF. Assume a TEM mode does exist there."
So the last discussion shows a contradiction - i.e. a structure like this cannot support TEM mode.

P.

hi
you can refer field and wave by d.cheng
bye

Status
Not open for further replies.