this is the final lecture on this introduction
to electromagnetic theory course you have
learnt in this course about electrostatics
about magnitude statics then we came to the
dynamics part and you learnt how electric
and magnetic fields can give raise to each
other through when the change time we have
also learn how to sustain each other and give
raise to ah ah disturbance that can radiated
that that can propagate and that is called
radiation no course on e m theory is going
to complete until we see how this radiation
arise this so in this final lecture i'm just
going to give you a qualitative description
of how you electromagnetic radiation arises
you all heard in your eleventh twelfth period
in particular in connection with both model
at any radiation radiates and therefore in
bohr's model and atom would be unstable if
that charge moving in the orbit radiated because
it accelerating
so what i want to show in this lecture is
how acceleration of charge least radiation
to start with let see y and non accelerating
charge should not radiates so let us look
at a charge q point charge q moving with constant
velocity v which is such i am going to focus
this lecture on magnitude of v being much
much much less than c which is the speed of
light 
in one of the previous lectures or assignments
you seen that a moving charge create a magnetic
field around it so this charge q which we
take to be positive suppose it is moving the
right direction it will have a b filled which
is coming out on top and going in the bottom
and as you go away field magnitude become
smaller not the less this is what it is and
to go a approximation i can take the e field
to be being readily out
if this is for v magnitude you much much much
less than c so that what you notice is that
the pointing vector s 
is such that it is does not take the power
away and therefore does not reradiate there
is another very cute way of looking at it
and that is this if this charge is moving
with velocity constant velocity v let us attach
a frame to this charge let me make a frame
by as red line x y z and this frame therefore
is also moving with constant velocity v and
here is my ground frame so with respect to
the is ground frame is frame is moving with
velocity v however in this red frame which
is moving frame a charge at rest and therefore
the electric field due to the this charge
is going to be radially awkward and there
is no magnetic field
and therefore no radiation so let's write
this no radiation in the moving frame however
this frame is moving with respect to the ground
frame is a constant velocity and therefore
it's an inertial frame and the physics in
the two frame has to be same and this therefore
this implies if there is no radiation in the
moving frame this implies there is no radiation
in the ground frame also thus charged moving
with constant speed does not reradiate let
us now show how and accelerating charge would
give out radiation so now what we want to
show is and accelerating charge gives out
radiation if you continue doing physics or
an advanced course in electromagnetic theory
you will see a mathematical radiate derivation
of this through potential and all that and
here is the description is going to be very
very qualitative
so let us for this understand to key properties
that i am going to use of radiation in a radiation
the electric field e and the magnetic field
b or both perpendicular to the direction of
propagation we have seen that in the past
two lectures number two if there is a point
charge a reading suppose with power p as you
go farther and farther away the same power
start going to a larger and larger area and
power per unit area is nothing but the pointing
vector which is the proportional to e square
so the pointing vector 
or power per unit area form a point source
of radiation is proportional to one over r
let us see pictorially instance from the point
source and this implies that the e is proportional
to one over r let us see pictorially if i
have a points source let's make it with green
out here then at a distance r if the radiation
is going out this way i would have an e field
either going as shown here or go into the
paper
in another words it is perpendicular to the
direction of propagation and e will be proportional
to one over r if i can show that an accelerating
charge give me a propagating disturbance which
goes as for which the e field is one over
r is perpendicular direction of propagation
i have shown in the radiation suppose this
charge at rest i take a charge at rest this
has an electric field i will make three or
four line lines like this 
and this e field is nothing but q over four
pi epsilon zero r square where r is a distance
and this field is radially out now suppose
this is step one step two gave and impulse
of very short duration tau to this charge
so that it gain a velocity v and again we
want to focus on the cases where the magnitude
of the velocity is much much less then this
field of light
so this charge now is moving with speed b
with velocity v it has been given this tau
impulse very duration for time tau let's see
what happens now so here was a charge initially
at rest and this field was going out like
this a making radially out and this has given
a k so that in time t it reaches here things
are little excoriated it reaches this distance
v t now in this same time t since the charges
in same position the field also has change
and v is very small though the field is going
to be redial about this position of charge
let me again write the same lines that i made
for charge and it at rest however this cannot
be redial all over the space or it cannot
be this red field all over the speed because
the propagation of finite speed of light
so this will become redial the red field exchange
only up to the distance c t so this distances
is c t after that for some period tau now
i don't know what the field is but certainly
need not be radial the reason is very simple
during tau that small time period the charge
was accelerating and therefore i cannot actually
attach an inertial frame to it if i could
attach in inertial frame to it i will see
the field in that has field exist in the now
ground frame but i don't know i cartinly no
because when it moving a velocity we have
certainly know that i can attach a frame to
the charge in which the field is radial and
since velocity small it remains redial in
a ground frame also i certainly know that
outside the seat of the field is redial again
this in between the two region which i am
showing through the greeni do not know the
nature of field all rights
so let's now make this picture again so i
have this black address charge and up to a
distance ct and little beyond that after that
the field is radial all over the place let's
do it on this side also so i will make this
circle is one circle like this around it there
is another circle like this outside the out
of the circle of the field radiant on this
side also this distance between the two circles
s c time tau the tau that small duration time
during which i give the impulse after time
t with charge particle come here this distance
between v t and now the field will be radially
out from this but only up to this inner circle
because that information that has moved reaches
only this part in between something else happens
now notice that in nexus equation we assume
that divergence of e integrated over surface
is equal to q over epsilon zero which is gauss's
law this remains in where no matter which
frame i am in so the number of lines if i
take number of lines representing the charge
remains the same outside and inside so the
only way they can be there therefore added
is that i connect then through this green
field out here green field out here green
field out here green field on the site so
the field lines are looking like this this
let me make them in one colour clearly like
this goes out goes out comes here like this
goes out and goes out like this and goes up
and you see this is line structure wheel on
the side is like this again when i looked
at the field inside it was redial field when
out sitting at the charge moving with the
constant velocity again whatever i saw in
that frame for small groosy i can say the
field is essentially the same in the ground
frame also in between i don't know the only
thing i know is that the number of lines should
remain the same outsider inside and therefore
this is the blue line show the way you only
way i can connect them only simplest way we
can connect them but if i connect them like
this something intrusting happens in this
region between two circle here you see the
blue line has a component which is perpendicular
to the directions redial direction so what
is happening
now as we gave the acceleration the impulse
this is small region which is of width c tau
is started propagating out this with the speed
c so there is this region corresponding to
size is to those times when the charge accelerated
that has the field perpendicular to the redial
direction of perpendicular direction of propagation
so we have established that there exists a
field in those times when the charge is accelerating
which is perpendicular to the direction of
propagation next you want to show that it
is one over r and therefore calculate the
power radiant
