Displacement current - Electromagnetic Waves Video Lecture - Class 12

hello friends this video on
electromagnetic waves part 4 is brought
to you by exam here calm please make
sure that you have watched all the
videos till part 3 before going ahead
with part 4 let us quickly discuss a few
points about the displacement current
so because displacement current is
something which is newly introduced to
you right so you are learning about
displacement current for the first time
so now let us quickly discuss
displacement current now if you consider
this capacitor because if I take the
example of this capacitor you will
understand it at its best because this
is the example where the ampère's
circuital law field right so now in this
case when you look at outside the plates
you have the current which is conduction
current because it is due to the
movement of the charges now when you
look at the area between the plates you
have the current that is displacement
current
now the displacement currents physical
effects I mean when I talk about the
physical behavior of displacement
current it is the same as that of
conduction current that means the it is
it behaves in a similar way as a current
behaves like the units to measure
displacement current would be the same
as that of conduction current all its
physical behavior will be the same as
that of conduction current the only
difference is that conduction current
arises from moving charges and
displacement current arises from
changing electric field otherwise they
both behave as current there is no
difference as such now when we talk
about but when we talk about static
electric fields static electric fields
means the electric fields are static
they are not changing with time so if
the electric fields are not changing
with time in that is displacement
current will be equal to 0 because
displacement current arises only when
electric field changes with time so for
time varying electric fields for time
varying electric fields
displacement current is nonzero that
means you have some value of
displacement Canada so they are can't in
certain situations there can be certain
scenarios where you have only conduction
current and there is no displacement
current for example in this case outside
the plate of the capacitor
you have conduction current but
displacement current is zero similar if
you look at the area in between the
plates of the capacitor your conduction
current is zero but you have
displacement current
there can be certain scenarios where you
have both conduction current as well as
displacement current in that window
scenarios the total current will be
equal to IC plus ID right so now if you
consider the modified law that is a
modified ampere Maxwell law using that
law if you try to calculate the magnetic
field at different point at the same
point of the capacitor considering
different amperian loop you will get the
same result I mean it will be consistent
right so now let us look at the
consequences of Maxwell ampere Maxwell
law so now as I mentioned before also
now if you look at these two setups in
the first setup what is your magnetic
field so in the first set of the
magnetic field is given by integration
of B dot DL is equal to MU knot I now
here what is nu naught I knew naught I
is mu naught I see now in the second
setup this is the first setup and what
is the second setup in the second setup
it is integration of B dot DL is equal
to MU naught IC plus ID so here IC is 0
but you have ID so that means in this
case in both the cases you will get some
value of magnetic field so your magnetic
field in both the cases will be equal to
MU naught IC divided by 2 pi R here it
will be B is equal to MU naught ID
divided by 2 PI R so you get consistent
values or
magnetic field at the same point of the
same setup even though you have
considered different Antarian lose now
what will be the value of the conducting
current and the displacement current
that depends upon the exact scenario
right because the total current has to
be the same so if I say let us suppose
if I say that the total current outside
should be equal to the total current
inside that means outside you have only
conduction current inside you have only
displacement running so your conduction
current and displacement current has to
be the steam because total current
should remain the same right so now what
was the final conclusion of this ampere
Maxwell log that means the what an
ampere proposed I mean wanted max will
propose at the very beginning Maxwell
proposed that a time-varying electric
field should generate a magnetic field
and that is happening now because if you
look at this example itself what was
happening there is electric field
between the plates the electric field is
varying with time so because of this
time varying electric field there is a
displacement current and because of this
displacement current you have this
magnetic field so that means a time
varying electric field is generating a
magnetic field so that means that final
conclusion is that a time varying
electric field can generate the magnetic
field and the time varying magnetic
field can also generate an electric
field so this was given by Faraday Lenz
law
similarly this was given by ampere
Maxwell
law so the final conclusion is that if
you have an electric field which is
changing with time it can generate a
magnetic field similarly if you have a
magnetic field which is changing with
time it can generate an electric field
so now it has become a two-way process
electric field generates magnetic field
magnetic field generates electric field
right so this is the main concept or
this is the baseline of electromagnetic
waves you will now you will see that you
will be even one
stand the concept of electromagnetic
waves very easily so here I have just
diagrammatically represented what I told
you just now this diagram represents
your Faraday Lenz law that is time
varying magnetic field produces
electricity the other one shows that a
time varying electric field that is the
current because of the current which is
flowing through the conductor is
generating a magnetic field now water
Maxwell's equations now Maxwell
contribute Maxwell's contribution to
modify this ampère's circuital law
became so significant that the set that
a set of four equations which were all
given by different different scientists
came to be known as Maxwell's equations
little surprising right but that is how
it is so the first equation is
integration of e dot d s is equal to Q
divided by epsilon not familiar to this
right what is it it is nothing but Gauss
law in electrostatics Gauss law in
electrostatics now there this has a
counterpart in magnetism which said
integration of V dot d s is equal to
zero and that was Gauss law in magnetism
so the next equation was nothing but the
Faraday Lenz law Faraday Lenz law which
stated that a changing of time varying
magnetic field gives rise to electric
field so the Faraday Lenz law was extra
Staz integration of e dot DL is equal to
minus D Phi by DP this Phi is nothing
but the magnetic flux changing with time
and what is this this is nothing but the
induced EMF because induced EMF is equal
to electric field into the path
traversed right so you got first second
third equation and the last but not the
least equation
is nothing but the Maxwell ampere law
that is integration of B dot DL is equal
to nu not IC plus mu naught epsilon
naught D Phi e by DT so this was ampere
Maxwell law and this was Faraday Lenz
law these four laws were together known
as Maxwell's equations because if you
look at these four equations they relate
electricity and magnetism very closely
to each other the first equation talks
about the surface integral of electric
field the second equation talks about
the surface integral of magnetic field
the third equation talks about the line
integral of electric field the fourth
equation again talks about the line
integral of magnetic field so you can
see that they are all counterpart of
each other and that is how it was seen
that electric field and magnetic field
are closely related to each other this
magnetic flux gave rise to electric
field here my electric flux gave rise to
magnetic field now in this now these
four equations related electricity and
magnetism to each other and also it was
experimentally found that this constants
epsilon naught and mu naught
what are these constants epsilon naught
is nothing but permittivity I spoke
about permittivity when I talked about
the lessons on electricity similarly
what is mu naught it is nothing but
permeability we talked about in in oven
magnetism lesson right now
experimentally it was found that C that
is the velocity of light is equal to 1
by root over mu naught epsilon naught so
this was an experimental finding so that
means we see that these Maxwell
equations not only relates electricity
and magnetism but it also relates ray
optics that is like optics so that means
electricity magnetism and optics they
are all related to each other
we are all interrelated so Maxwell's
equations are very well-known and they
came to be known as Maxwell's equations
because of Maxwell contribution in
modifying the ampère's circuital law so
and now we reach towards the end of the
topic on Maxwell's work and Maxwell's
equation so what was the final
conclusion the final conclusion was that
a changing electric field produces a
magnetic field
similarly a changing magnetic field
produces an electric field now based on
this we will now try to understand what
are electromagnetic waves thank you
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