In last few lectures we investigated propagation of an electromagnetic wave inside wave guiding
structures. First, we investigated propagation inside what is called a parallel plane wave
guide and later we derived the fields inside a rectangular wave guide. Of course the approach
which we took in two cases was different. In first case that is for parallel plane wave
guide, we visualize the propagation of electromagnetic wave as the propagation of uniform plane wave
by multiple reflections at the two conducting boundaries of the parallel plane wave guide
whereas in case of rectangle wave guide we took the mathematical approach that is we
simply said if you wanted to have a transverse electric or transverse magnetic field, mathematically
just solving the wave equation in satisfying boundary conditions what kind of fields we
would get. The visualized wave which we had in case of parallel plane wave guide they
were the physical understanding of what kind of field can exist inside a wave guiding structure
and from there only we understood that if we go perpendicular to the planes, the conducting
boundaries then we will have the wave which will be standing wave kind of waves whereas
along the plains you will have traveling wave and using this physical understanding we can
appropriately write the mathematical functions for electric and magnetic field inside a rectangular
So, in one case we had physical visualization of the phenomena in other case it was a purely
mathematical approach and now we must verify that mathematically which we did blindly for
the rectangular wave guide, does it give me the fields which me have derived from the
physical understanding for the parallel plane wave guide. So, essentially what we have to
do is we have to establish that the fields which we got for rectangular wave guide, if
we take the limiting case then the fields must represent the fields which we got for
the parallel plane wave guide.
So, now what we will do is we will do an exercise of showing that these fields which we got
for the rectangular wave guides indeed represent the fields which we got for the parallel plane
wave guide is the limiting case when one of the dimension of the wave guide becomes infinity
and then we are also ask a question what happen to the mode which was TM 0 mode which became
the TEM mode in the parallel plane wave guide. What happen to that mode in the rectangular
wave guide? Does it mode now exist inside rectangular wave guide or it exists only inside
the parallel plane wave guide?
So, let us take first the second question that is does the transverse electromagnetic
mode exists inside a rectangular wave guide. This we can argue physically that if we consider
a rectangular wave guide and let us say the, we are taking whether transverse electromagnetic
mode would exist inside the structure that means for this mode the electric and magnetic
field both are perpendicular to direction of propagation. That means they must lie in
this plane, the cross sectional plane that is the plane of the paper. Now we know that
magnetic field lines must close on themselves and all these magnetic field lines are now
lying in this plane that means they must form the closed loops in this plane. So, the magnetic
field lines in the transverse plane must look like that.
However, if the magnetic field lines are like this then we know that there has to be a current
enclosed by this magnetic field lines. So, there must be a current flow something like
this which is enclosed by the magnetic field lines then and then only this magnetic field
lines can survive. So, there are two possibilities one is we have a conduction current which
is flowing perpendicular to plane of the paper and that is enclosed by this magnetic field
line, so they can survive or there could be displacement current which will be perpendicular
to the plane of the paper and that will be enclosed by the magnetic field lines, so the
magnetic field lines can survive.
Since, we do not have any conducting medium inside this wave guide, this wave guide is
completely hollow, it means it is filled by pure dielectric, there is no possibility of
conduction current enclosed by this magnetic field lines. The conduction current is 0 inside
the rectangular wave guide, so only possibility which can exist with we have displacement
current to support this magnetic field lines and the displacement current must be flowing
in that direction but the displacement current would require the electric field which will
be going in that direction which we all denied for transverse electromagnetic mode but transfer
electromagnetic mode we say the electric field also lies only with transverse plane that
means it does not have a component perpendicular to the plane of the paper, if that is so then
we cannot have the displacement current inside this wave guide which is in this direction.
So, neither we have conduction current flowing this way nor we have displacement current
flowing this way, so there is no current which is flowing perpendicular to the plane of the
paper and if there is no current that cannot magnetic field lines because by MPS law this
magnetic field lines must be related to the current enclosed. So, that means these fields
which are lying in a transverse plane they cannot exist because there is no current to
support these magnetic field lines that means this mode, the transverse electromagnetic
mode cannot exist inside the rectangular wave guide.
So, this mode TEM mode doesn't exist inside this wave guide. There one can ask the question
how was it existing in the wave guide which is the parallel thin wave guide and before
you get into that question let us first take the parallel plane wave guide as a limiting
case of the rectangular wave guide. So, if I take this rectangular wave guide in which
the T 1 0 mode is existing that means electric field is like this and if I make this B is
equal to infinity, if I push this wall to infinity essentially I will get a structure
which will be the parallel plane structure, this plane and this plane wave is going to
traveling in the Z direction and these to walls are pushed to infinity, so as a limiting
case of the rectangular wave guide by pushing these two walls to infinity, I can get the
fields for the parallel plane wave guide.
And in this case since the electric field is like this and the wave is going to propagate
perpendicular to the plane of the paper, this mode essential would correspond to the TE
mode. So, we have now by pushing these things for T 1 0 mode, if I push this field it walls
to infinity then I will get a geometry which will be the parallel plane geometry and for
this geometry, electric field is oriented like this so that will give me the transverse
electric mode. So, what you are saying is if I take this wave guide and push it to infinity,
so these are the two walls of the wave guide is my coordinate axis.
This is the direction which is the Z direction, this is the x direction and I am pushing these
two walls to infinity and the electric field now is oriented in this direction which is this way. So, I have
a component which is Ey and I have the magnetic field which is Hx an Hz for the T 1 0 case.
So, if I look at the fields which I had for TE 1 0, I have Ey component I have Hx component
and I have Hz component and these fields were constant as the function of Y. Same thing
we can get now for the infinitely extended wave guide in Y direction that if there are
no boundary conditions to apply in this direction these fields are infinite then this field
is constant in that direction that was the precisely the field we used to get for parallel
plane wave guide. So, indeed we can take the transverse electric 1 0 mode, make this boundary
to go to infinity but since we do not have any dependence of be here, what that means
is these fields are the same fields as I would get inside a parallel plane wave guide for
a transverse electric 1 mode. So, these fields are TE 1 0 for rectangular wave guide but
these exactly the same the explanation I have for TE 1 mode for a parallel wave guide.
So, we have a situation here which is TE 1 mode for which the fields identical, two these
fields which are T 1 0 mode for the rectangular wave guide. So, here you have the magnetic
fields which are having X component and Z component then Ey will be in this direction.
So, you are having now the Z magnetic field which is in this direction, so as the limiting
case of the TE 1 0 mode we can get the transverse electric mode, lowest order transverse electric
mode which is T 1 mode and the fields will be exactly same as what we go for T 1 0. The
another mode which we had was the transverse electromagnetic mode for which the electric
field was not tangential to the boundaries, it was perpendicular to the boundary. Magnetic
field was tangential to the boundary and we saw that was the mode which was not dispersive
and which traveled as if the conducting boundaries are not existing and that is mode which was
the TEM mode.
So we had a situation like that if I take a parallel plane wave guide like that and
if this is the electric field E and this is the magnetic field H then the wave is going
to travel in this direction Z and then this wave travels without any variation of electric
and magnetic fields that we saw earlier because neither H requires a boundary condition to
be satisfied, this is tangential you can always surface currents nor the normal component
of electric field needs any boundary condition to be satisfied, you can always have the surface
charges induced to compensate for the normal component of the electric field. So, this
mode which was the transverse electromagnetic mode was existing inside and now one can ask
a question, if this was the limiting case of the rectangular wave guide, how come this
mode exist in this but when we take the rectangular wave guide this mode doesn't exist. But one
can argue since the magnetic field is in the direction and since this plane is extended
in Y direction, one can say that is magnetic field lines essentially close at infinity
and they enclose these conductors, these conducting boundaries which have the current flowing
on them, the surface currents.
So, in the case of rectangular wave guide where these boundaries are finite, this magnetic
field lines they have to close on themselves and that's why the current is not enclosed.
So, this mode cannot exist inside rectangular wave guide but if I take a parallel plane
structure then these magnetic field lines will close at infinity and they well enclose
this conductors and that's why this mode can exist inside the parallel plane wave guide.
This is the mode which is as we saw in case of two conductor system like a coaxial cable
or transmission line, this mode propagates. So, whenever we have two conductor system,
the lowest mode which will propagate will be TM mode, however if you go to the rectangular
wave guide then the lowest mode which will propagate will be TE 1 0 mode. So, we have
very important conclusion to draw that whenever we have the hollow structure, hollow pipe
and the wave guide, the transverse electromagnetic mode cannot exist which is non-dispersive
because it was a very special mode, this mode is not supported by the rectangular wave guide
and that's why we have all those problems of dispersion and so on inside a rectangular
wave guide. But that is the structure which is more physically realizable structure, you
should remember that. The parallel plane wave guide is still a structure which is infinite
in extent. So, we cannot realize this in practice, it is good for understanding but when we want
to realize the structure in practice it is the rectangular wave guide which can be realized
in practice not the parallel plane wave guide.
So, whenever we have a physical structure which is rectangular wave guide, we will always
have a cut of frequency associated with that and we will always have the problems like
dispersion and so on associated with that. With this understanding now let us try to
see the currents which get existed on the walls of the wave guide which actually support
this fields inside the wave guide, so whether you take parallel plane wave guide or you
take rectangular wave guide what is the mechanism by with this fields are supported inside wave
guide? What are the sources and the sources are nothing but surface charges and surface
current which lie on the inner surface of the wave guide. So, as the wave travel even
the surface charges keep moving to accumulate at different location as we will see little
later and these charges and surface current support the electrical magnetic fields inside
the wave guide which are responsible for carrying power inside the wave guiding structure.
So, what we will do now we will try to visualize first the fields which would be there inside
the wave guide and then will try to visualize how the currents are distributed on the walls
of the wave guide. So, let us take for the simplest case which is the TM case and the
parallel plane wave guide.
So, let us see I have a parallel plane geometry and let me Orient the planes, so these are
the two conducting planes the energy is going to propagate in this direction and if I take
the TEM mode, we saw the TEM mode the electric field is perpendicular to this. So, if I say
this is my x direction, this is y direction then we had the electric field Ey which was
some constant e to the power minus j beta z and we had a magnetic field which was a
Hx which is c upon eta e to the power minus j beta z. If I visualize these fields is say
if I really want to find out how these fields are going to be either the function of space
and time inside the structure, first what we do we freeze the time. Remember all this
quantities are intrinsically functions of time and they are having it harmonic variation
as a function of time, so e to the power plus j omega t is implicit in all these terms.
So, as such these fields are going to vary as a function of space and time. So, if I
stand at particular location the fields are going to vary sinusoidally as a function of
time. If I freeze time we are bringing instantaneously look along the wave guide, I will see the
field variation which will be given by that. So, essentially what we do to visualize these
fields in three dimension first we do is freeze time that means make this quantity constant
and then without losing generality we can say let make T equal to 0. So at that instant
I want to see how the fields are distributed in space. Once I get those field distributions
in space then we simply say that these fields will be moving with the velocity which is
the phase velocity for the mode to then the let the field drifts inside this wave guide
with the phase velocity. So, when we visualize these fields essentially we try to visualize
the special variation of the field at some instant of time and without losing generality
we can take that time is equal to 0. So, if I take the T is equal to 0, if I freeze time
then the field visualization will be simply a real part of this quantity which is real
part of c e to the power minus j beta z and this will give me again real part of c upon
eta e to the power minus j beta z. So, Ey has a variation which is real part of this
which is c into cosine of beta z, Hx will be having the same variation c upon eta cosine
of beta z.
So, if I consider this point as z equal to 0, this variation is beta z and the wave length
which we have here or the phase constant is beta, so the corresponding wave length let
us call in general that is the guided wave length in the direction of wave propagation.
So, this field has the period, special period which is equal to the guided wave length and
at z equal to 0 this field is maximum. So, it is maximum here and it is not varying as
the function of x or y, so the fields are constant everywhere. So, the field is varying
as a cosine function along the z direction. So, it is maximum here, so if I take here
this point j z equal to 0, so it is maximum and then it goes like that either I move along
the z direction like a cosine function where this is 0, this quantity will be lambda g
by 4 that this function will go to 0. If I go again lambda g by 4, this function will
become negative and so on.
So, this filed now I can visualize as the electric field which is constant everywhere,
so this is the field distribution for the electric field is like that which is same
everywhere and so on. And the magnetic fields are horizontally oriented and there again
having the same amplitude all across, so this is the direction of the magnetic field. So,
though direction is taken appropriately so that E cross H gives me the power flow which
is in this direction. So, this is magnetic field which is everywhere as distributed,
so this is my H vectors and this my E vectors. And at to maximum here, as I move to lambda
g by 4 along the direction of wave propagation these fields will go to 0 then again they
will reverse the direction after lambda g by 4, go to maximum when z becomes equal to
lambda g by 2 and so I got a variation which is if I look like that, if I turn it electrical
field is maximum here slowly reduces, goes to zero, changes a direction again increases
maximum negative. So, start from here goes to 0, changes direction increase again maximum
that's the where electrical field is distributed. You can see here the rod shear which is standing
of different heights, it is maximum here at z equal to 0, the height of the rod goes to
0 at lambda g by 4, the direction of the rod is reversed. And again the amplitude becomes
maximum, when I go a distance of lambda g by 2.
Same thing happens here for the magnetic field lines which are now like that, so they are
stacked. This will look as if you are having a layer of the magnetic fields which are oriented
this way as stack and again there variation is will be exactly same that when this field
goes through 0, the magnetic field also will go to 0 and so on. So, it requires little
imagination to really visualize these fields but with little practice one can definitely
see how the electric fields and magnetic field are distributed inside the wave guide.
Now, if we know that the magnetic field is like that the current which is going to flow
on the surface of this conductor is related to the magnetic field, tangential component
of the magnetic field. The N cross H gives me the surface current on these conducting
walls and since we are considering here the ideal conductors, essentially if I calculate
N cross H that is the current which is truly confined to the surface of this parallel plane
wave guide. So, if I consider this surface then the normal will be coming outwards, so
this is my normal unit vector whereas if I consider this plane then the normal which
will be coming out of the conducting surface will be this now.
So, the unit vector outward normal for the lower plane will be going upwards, the unit
normal for the upper plane will be going downwards and now you can calculate N cross H everywhere.
So, this is direction of H, this is N, so if I calculate N cross H at the point I will
get the direction of the surface current which will be along the direction of the wave propagations.
Similarly, say on this surface the current will be going in this direction because I
get N cross H whereas if go to the this surface then I will get N cross H, N is now down words
H is this, so I will require N cross H which gives me the current which will be coming
So, on the lower surface I get a current which is going this way, this is my surface current
where on this surface the current will be flowing this way which is Js and it will be
having a same variation as the variation of the magnetic field that means it will be maximum
here after the distance of lambda g by 4 this current will go to 0 and so on. So, in a two
conductors system, it gives you the current flow in the direction in which the wave is
propagating. I have a current flowing this way, I have a current flowing this way and
precisely that's what we are essentially used to that when we have a two conductor system
like a coaxial cable, we connect a voltage source and the current goes inside the conductor,
the current returns by what is called as a ground path. So, we see that the current goes
inside from one terminal and current comes out side from the other terminal. So, in that
situation which is like a two conductor system, the direction of the current flow which we
have for this mode, TM mode keep that mind is same as the direction of the wave propagation.
So, the current is going, current is returning from here.
Question one can ask is if the wave is propagating in this direction, is it always true that
the current has to flow in the direction of the wave propagation and invariably we get
the answer which is wrong and that is since we always discuss the transverse electromagnetic
mode that's what we are used to when we go to low frequency circuit immediately we jump
to the conclusion that yes since the wave is moving in this direction, the power is
flowing in this direction, the current must flow in that direction.
Let us look at the parallel plane wave guide but let us take the mode which is TE 1 mode
and let us see what will be the direction of currents in field in that wave guide. So,
let us consider the structure which we have got this is the T 1 mode and this is parallel
plane wave guide. As we saw that the fields for the parallel plane wave guide will be
identical to this, so firstly the electrical field will be y oriented, they will have variation
which will be next direction and they will be varying again in z direction with phase
constant beta so in this direction if I look at the field variation and if I write down
the expression for this, I will get again in z direction also.
However to visualize these fields, as we did in the previous case let us take amplitude
of this field that is real part of this quantity and plot that as a function z, x and y, you
will get a three dimensional picture of the fields. Before we do that however let us try
to take this j and represent that along with this because j is e to the power j pi by 2,
so minus j will be e to the power minus j by 2.
So, if I take this field expression and write that I get this quantity Ey that is equal
to let me put this whole quantity as some constant, at the moment we are only interested
in finding the variation of the field in X and Y, so let there be some constant here
expect j we are going to put at this point. So, let us say I have some constant here some
A sin of pi x by a and I write here e to the power minus j beta z and I take this minus
j up so this will be equal to minus j pi by 2. So, if I want to get the instantaneous
field as a function of x y z at a real part of this quantity, so the instantaneous value
the electric field that will be real part of Ey that will be amplitude A sine of pi
x by a. Cosine of this quantity, this quantity and that will be equal to the sine of beta
times z where you have a phase difference here of pi by 2. So, you have here sine of
beta into z which we can write down explicitly in terms of the guided wave length. So, this
we can get is A sine of pi x upon a sine of 2 pi by lambda g into z. Same thing I can
do for this magnetic field also, so this quantity again there is omega epsilon, the omega nu.
So, I can say this is another constant for the magnetic field, so Hx I can write down
the instantaneous value that will be real part of Hx which will be some constant B sine
of pi x upon a and this quantity is same again we can take a minus j up there, so this will
be sine of 2 pi by lambda g into z. And I can get again the instantaneous value for
the magnetic field z component and there is no j here now, so if I take real part of this,
this will be simply cosine of beta z so the real part of the Hz that will be equal to
is constant C cos of pi x upon a cos of beta z, this is 2 pi by lambda g to z. So, these
are the fields which are now if I freeze time and if I take that T equal to 0 then at that
instant the field along the wave guide will be given by this expression. So, in the z
direction as we can see the fields are sinusoidal with a period, special period which is lambda
g however these two are in quadrature that means wherever Hx is maximum, the Hz is 0
and wherever Hz is maximum Hx will be 0.
So, in space we are having two components now, the Hx component and the Hz component
and Hx component is having a sine variation. So, if I take this point z equal to 0, Hx
is 0 at this location but Hz is maximum at this location. If I have go a distance of
lambda g by 4 on this, at that location Hx will be maximum but the Hz is will go to 0.
So, if I see from the top it will appear here the Hx was 0, only Hz was here. As it is moved
to a distance of lambda g by 4, the Hz becomes 0, only Hx become maximum so the magnetic
field totally become like this along this direction.
As I move further again by lambda g 4 again Hz will become maximum, Hx will come 0. So,
what you find that here we have a function which is cosine with that means if I take
this as plus direction, so here I have a magnetic field like that. On the opposite wall magnetic
field will be this the cosine function, so z equal to this quantity, this variation as
a function of x. If I plot this, this is the one which in the x direction is going to be
like this, z direction the variation is periodic with lambda g but in the x direction this
is maximum at x equal to 0, at x equal to a with opposite sign and 0 at the center.
So, the magnetic field lines are maximum here and no component of the magnetic field Hx
at this location, so the fields are this.
If I go to the distance of lambda g by 4 in this direction, at that location if I see
here the Hz would go to 0, Hx will be maximum but the Hx is a having variation of sine of
pi x upon a. That means Hx is maximum at this location but it is not maximum on the walls,
this function is a sine function. So, it is 0 here, 0 here and will be maximum here and
that will be the direction for Hx which would be like that.
So, if I see from the top I see situation like this for the parallel plane wave guide,
so if I am seeing on the top like that the magnetic field is z equal to 0, the magnetic
fields are like that, like that here. When I go to distance of lambda g by 4 this thing
has gone to 0 and Hx is become maximum so that is oriented in this direction. Now it
is matter of a little imagination since we know that magnetic field lines close on themselves
essentially we have a magnetic field loop which is created like this, so we got a magnetic
field lines which will go like that. And if I go further lambda g by 4 from here the direction
will be reversed, if I go further in this direction, this direction is x remember so
again I get the magnetic loop which will be like this and so on.
If I complete this if I now say the other way a wave guide which is running from minus
infinity to infinity, essentially I will get the loops of the magnetic field lines which
will look like that where this separation will be equal to lambda g by 2. So, if I look
at the wave guide which will look like that this is the parallel plane wave guide, the
magnetic fields lines look like rolled carpets which are stacked inside the structure and
they are of infinite length which are perpendicular to the plane of the paper. That's the way
the magnetic field lines will be distributed. What about the electrical field? The electrical
field has a variation in z direction which is same as this but it is oriented in y direction,
so if I consider this it is having sinusoidal variation in this direction but oriented this
So, if I see from the top then the electric field lines will be perpendicular to the plane
of the paper and behavior of this Ey and Hx is identical that means wherever Hx is maximum,
Ey is going to be maximum only thing it has variation, it is sinusoidal variation so it
has identical variation 2 Hx.
So, if I look at the Hx component which is this component, here is Hx component which
is maximum, so the electric field also will be maximum at this location but electric field
is always oriented in y direction. So, I have the electric field which will be like that
and if this is the direction positive direction for z in which the wave is propagating again
you can have E cross H. So, if this is direction of the magnetic field the electrical field
should be going inwards so E cross H gives me the pointing vector so that is direction
of the electrical field and this electric field reduces to 0 at this location, so I
have electric field becoming lesser and lesser as I go this direction. Similarly, it's becoming
lesser and lesser because the tangential component should become 0 so this becomes less here,
less here and so on.
Again where I go on this side the electrical field now will be coming outwards and amplitude
will increase again, so here the size of the circle tells me the strength of the electrical
field. So, the electric field will be distributed maximum where this Hx component is maximum,
so this is more like rods which are inserted in the rolled carpets that is the electrical
field vectors. So, if we want to visualize in the three dimensional kind of fields, the
electric field will be the stacking of the rods of different diameters where the diameter
represent the strength of the electrical field and the magnetic field will be likes stacked
rolled carpets which will be like that.
Once we get this magnetic field things which is now a rolled carpet which we have got which
we have seen from the top the magnetic field lines like that, now we can ask what kind
of currents are going to flow in this. Say now the currents will be related to the tangential
component of the magnetic field on the walls and the tangential component of the magnetic
field which is this on this wall, these two walls is only z component, on this wall there
is no x component.
So, on this wall the unit normal will be going inwards so this is my m, for this wall this
is m. Here the magnetic field is going tangential to this which is in this direction, z direction,
x direction magnetic field is 0. So, on the walls if I see I have only magnetic field
component which is z component, if I calculate N cross H this is N and this is H. See, if
I go from here to here the N cross H in this direction I will get now the current direction
which will be tangential to this surface current that's what we are talking about but that
will be now flowing in the y direction because normal is in x direction and the magnetic
field is in the z direction, so N cross H if you take that current flows in the y direction
which is this direction.
So, we have now the surface current which flows into this, so if I take again and this
is my unit vector, this is my magnetic field which is like that okay. I take m cross h
which will be going from this to this, I get the direction of the current which will be
surface current which would be like this, it is Js and this is Js. So, very important
note now is compared to the TEM case that's the surface current is going to flow in the
y direction that is very important. So, we have here surface current in y direction again
it will have a variation which is sinusoidal in z direction but there is no current flow
in z direction that is the important thing to note but the wave is traveling in the z
direction, if the wave is traveling in z direction the power is flowing in z direction.
So, what we now find something very interesting that the power flow there is no component
of current, surface current in this two conductor system in the direction of the net power flow.
The current flows in this direction but the power flow in this direction, so the notion
which you have at low frequencies that's in the power is going inside the system, the
current must be flowing in the same direction that is completely wrong in fact the direction
of current flow and power flow have nothing to do with each other. The current may flow
in some arbitrate reaction and the power may flow in some other direction. In fact it will
be also immediately clear to us that where is the power flowing, where is power. The
ideal conducted doesn't carry in any power inside; the power is only between these two
conductors. The power is carried by the fields which are trapped between the conductors that's
what is carrying power to support this field we required the currents, so the currents
are not carrying power. The power is carried by fields so there is no reason why the current
should flow in same direction which the power is flowing.
However as I have mentioned at low frequencies we normally have a wrong notion that since
the power is flowing inside the circuit, the power is carried by the current, the power
is carried by the chargers. So, we get a wrong picture that the currents have to flow because
the current is going to carry power in fact this is now a better understanding which says
that power flow is because of the fields and not because of the current. So, the current
may flow in some arbitrary direction and in this case you can see it actually flows perpendicular
to the direction of the power flow. So, the power flows in z direction and the current
flows on the surface of these two conductors which is in this direction. So, the notions
normally which we will have at low frequency circuits, they come from the transverse electromagnetic
wave though we don't say that explicitly there because that time when we talk about a simple
circuits, we do not get into the complications of the field distributions but intrinsically
we assume that the field which are carried by the electrical circuit is a transverse
electromagnetic field, so we have certain notions which we build for the electrical
circuit and they come essentially from the natures of transverse electromagnetic wave.
As soon as you make a departure from the transverse electromagnetic wave to a transverse electric
or transverse magnetic then all those notions completely break down and then we get much
global picture of propagation of electromagnetic waves and the currents and the distribution
of charges and so on at for various configuration. So, with this understanding now for the current
flow on this parallel plain structure which is rather simplest structure, now we can discuss
the field distribution inside the rectangular wave guide which is more practically realizable
structure and then again we will see the current flow on the wave guide surface for rectangular
wave guide and then we will have little more advance things like calculation of losses
and other things for rectangular wave guide.
So, let me summarize what has been discussed here essentially we saw that the transverse
electromagnetic mode cannot exist inside a rectangular wave guide and that we showed
from the physical arguments then we also showed that if you take a rectangular wave guide
and push one of the dimension to infinity then the field we get for rectangular wave
guide, they are identical to what we would have got for parallel plane wave guide. Then
we developed a mechanism of really visualizing these fields inside these wave guides.
So, we saw two cases one was the transverse electromagnetic wave inside a parallel plane
wave guide other was T1 mode inside a parallel wave guide and then we saw something interesting
that the direction of the current flow on the surface of the wave guide need not be
same as the direction of the power flow. The direction of the current and the power flow
are same for only transverse electromagnetic case. However if you go to general mode then
the current might be flowing in different direction and the power flow which is due
to the fields trapped between the two conducting boundaries could be in some other direction.
So, in next time we discuss in detail, the fields and the power flow inside a rectangular