in this section I will discuss about the
Faraday law and of electromagnetic
induction what it states it states that
whenever the magnetic flux linked with
a coil it change an induced EMF is
produced in the coil and it will last as
long as the change in the flux continues
so this is the point about the faraday law
and what is the 
mathematical form of it the EMF is
directly proportional to the time rate
of change of the magnetic flux and is in
the opposite direction according to the
lenzs law right so e that is equal to
the closed path integral of e.dl is
equal to minus del Phi B upon del T here
in this you see that this is a coil and
this is a magnet bar when basically it
moves forward and backward direction it
basically changed the flux associated
with this coil right and the two ends
basically of this coil is connected with
the galvanometer so when the flux change
here right associated with this coil EMF
which produce inside it produce the
deflection into the galvanometer so this
is basic idea of the Faraday law... right
so let us see how did Faraday's law can
be converted into the differential form
by using the Stokes theorem so you have
seen here that there is a open loop or a
coil right a bar magnet
the magnetic flux associated with the
coil it changes... then an EMF basically
produced inside the coil this is the
point so it is not possible if you keep
the bar magnet at fixed position right
here this is N S and this is equal if
you fix it here and magnetic field lines
magnitude is not changing then no e-m-f
will produce inside the coil it will
produce only then you move the bar
magnet into the forward and backward
direction so that is shown by the D
Phi B upon dt right so Phi B is the
magnetic flux first of all we have to
define the magnetic flux here Phi B is
the magnetic flux mathematically that
can be defined as beador tiers either
with the closed surface integral or open
surface integral but now the point is
here that how you will determine that
you have to consider here closed surface
integral or the open surface integral
this is the physical situation do you
know this is a circular ring a circular
loop or a coil the central part of it is
open or closed do you know that is open
so it means the surface of the coil is
open so the area for the flux the flux
passing through the open surface so
which type of area you will consider
open or closed obvious you will consider
the open surface so Phi B is equal to
open surface integral this Phi B is
equal to open surface integral of D dou
Venus right so that is written here this
B dot DL with open surface integral is
for the magnetic flux and rate of it
they upon DT this if I differentiate it
with respect to the time it means flux
is changing flux is changing and because
of that EMF is producing inside the
current loop right that is defined by
the closed path integral e dot DL while
the closed path integral because you
know on this is a circular coil right
and by changing the magnetic field right
associated with it it produces an EMF
inside the coil that means flow of
charges so because of the flow of charge
is because of the current and electric
field will develop right by this way you
can so this is center of the coil this
is the electric field tangential to the
circular path here this is e like this
way
if I consider a small segment here of
this circumference that will be deal if
I write it to actor DL then it will in
the same direction as of the electric
field right so e vector P and vector DL
both are parallel so closed path
integral of e dot DL what it signifies
right it signifies the EMF the potential
basically which develop across the ends
of the coil right if this is the coil
the one end is a and second end is B
right like this way number of turns so
magnetic flux is changing associated
with this coil and as a result the two
ends of this square write a potential
difference will generate and you can say
that the current is flowing here that is
basically the farad Allah but the
purpose is that we have to convert this
formula which is written here into the
differential form right so what we are
doing we are just applying the Stokes
theorem the Stokes theorem says that
closed path integral of the vector E is
equal to the open surface integral of
the curl of that field del cross e DS
right so in the left hand side the value
of e dot DL here is equal to the open
surface integral this del cross e dot Da
is right
no DS minus D upon DT and this b dot d
is right so now you can see here that
this is the open surface integral this
is also open surface integral now you
can compare both this side right so this
is now one more point here that this is
the open surface integral V dot d is now
let me know that this is the circular
coil in which the magnetic field passes
right so here what is constant magnetic
field is constant or the area of this
coil is constant obviously the area of
the coil is constant B is variable right
so differentiation of B with respect to
time time varying magnetic fields you
have observed here so this quantity
basically comes in to the left hand side
by this way right so again there are two
factor one is in bracket and second is
the area of the coil you know that area
of the coil is fixed that is not
variable that cannot be 0 if you are
applying the farad illa dear so this
quantity may be 0 so either this factor
or this factor is 0 area cannot be 0 so
you have this portion that this quantity
is equal to 0 when this del cross E
del cross e + DB upon del T this is the
LP 1 del T is equal to 0 and after
simplification opt you can see here that
this can be written as one of the curl
equation del cross e is equal to minus
del B upon del T so this is the possible
wave to convert Faraday's integral
equation into the differential form here
that integral equation is this one and
differential form you can see that is
this one del cross e so curl of the e it
means that you had considered here this
circular coil right and closed path
integral of e dot DL signifies there
this is equal to this if you take the e
tangential here of this tangential
tangential at this point so this total
right here OTL over this closed path is
equal to thee if you consider a small
small curl inside it Ed's head to all
them then the sum of these curl will be
equal to thee this one that is e dot DL
right a pictorial theme of that some of
these small small curve if you add that
is basically equivalent to this one
right so this is the meaning of a dot DL
and you are writing here this e don't
DL is equal to open surface integral
curl of e I am writing again it the e
dot DL is equal to open surface integral
sum of integral means some of the is
more current del closed
e B is right this is the meaning so this
was the possible right
