Biot Savart Law Video Lecture | Physics Class 12 - NEET

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I hope the concept of magnetic field or
the magnetic force experienced by a
charged particle in a magnetic field is
clear to you so now we will study about
a new topic that is the magnetic field
due to a parent item conductor till now
we studied what is the force experienced
by a charged particle when it comes to a
magnetic field that which is produced by
some other particle the magnetic field
was an external magnetic field but now
we will see what is the magnetic field
that is produced by a current carrying
conductor so now we will concentrate on
the current carrying conductor which
produces the magnetic field right so we
will see how do we calculate that how
much magnetic field will be produced due
to this current a conductor so called
this game of the biood severed law this
was another law which came up to
describe the magnetic field produced by
a current carrying wire well then now we
have what we were concentrating on the
magnetic force which a current carrying
wire will experience when it is placed
in an external magnetic field now we
will see what is the magnetic field that
is produced by a current carrying wire
so for that that came up the biood
severed law which tells us that the
magnitude of magnetic field is
proportional to the current I the length
element DL and inversely proportional to
the square of the distance R now what is
this this C's asked let us suppose if I
have some conductor carrying current
this is a current carrying conductor so
if I consider a small element let us say
DF of this conductor and I have to find
out the magnetic field produced by the
the doctor at some point C P and this
point P is located at some distance R
from the small element DM so in this
case the small magnetic field which is
produced at Point P due to this small
element DL will be hobart this small
magnetic field is proportional to the
current I which is flowing through the
conductor it is also directly
proportional to the length element that
is the small part of the conductor and
this is inversely proportional to the
square of the distance of this point
from the conductor that means four more
the closure the point is more as the
magnetic field that is very obvious also
because for any current carrying
conductor wire the region surrounding it
will have magnetic field so if you go
far away from the wire your magnetic
field will gradually gradually reduce to
zero that means as the distance of the
point increases the magnetic field
decreases right so taking into
consideration these things we found out
an expression for magnetic field and the
law also told that it's Direction is
perpendicular to the plane containing DL
and I that means it is perpendicular to
a plane which contains DL and I so that
means it has to be cross-product of DL
and I only in that case the direction
will be perpendicular to the plane
containing the Elega that is in
accordance with the definition of
cross-product right now considering
these two points both the magnitude as
well as direction we can see that DB is
directly proportional to I BL this
directly proportional to IDL divided by
R squared this is an accordance with the
magnitude now when we take into
consideration the direction also then we
can see that it is directly proportional
to
applause I and since we are multiplying
our so we can multiply the denominator
also so it is equal to this therefore we
can say that now in order to remove this
proportionality we need to introduce a
constant so a constant was introduced in
this form u naught by 2 pi I DL plus r
divided by r 2 now what is this mu
naught by 4 pi mu naught by 4 pi was a
proportionality constant where mu naught
is nothing but the permit permeability
of vacuum this is nu naught mu naught
was the permeability of vacuum now you
must must be thinking what is
permeability now like how in case of
electrostatics you had epsilon right 1
by 4 PI epsilon naught right so what was
that epsilon naught that was
permittivity of free space similarly K
mu naught is permeability of these space
now we will talk about permeability we
will talk about magnetic permeability in
our next lesson when I will deal with
this in detail so as of now you can just
know that so from here what do we get
the magnitude of magnetic field will be
equal to I DL so DL cross R becomes ie
DL and sine theta so we can make it as
IB L sine theta divided by R square
because this will be IB is R sine theta
divided by r cube so that R and 1 I will
get cancelled so it will be this much so
therefore this is your magnitude now
here mu naught is permeability of vacuum
and mu naught is equal to 4 pi into 10
to the power minus 7 this is the value
of Nu naught Tesla meter per ampere so
this is the value of mu naught so you
can just replace mu naught by 4 PI by 10
to the power minus 7 so this this is the
law now we do not have any proof
this law as such but this is the law
which tells us the magnitude as well as
direction of the magnetic field produced
by a current-carrying wire now how will
you find the direction of the magnetic
field in this case you will apply the
same right-hand rule but in right-hand
rule now it is DL cross I so all your
four fingers should curve from DL
towards I and in during that time the
direction of your thumb will tell you
the direction of magnetic field right so
I hope it is cleared by its separate law
so now I will show you how is
electrostatics analogous to magnetism
now you will see this bias separate law
has so much of similarity with the
Coulomb's law of electrostatics so let
us have a comparison of the voters here
comes your by eight separate law and
Coulomb's law so when I talk about by a
separate law in biood separate law the
force which we are talking about is a
long-range force what do you mean by
long-range force long-range forces is
the one where as the distance increases
the force decreases that means the force
experienced at large distances will
gradually decrease and the experience
will increase as we come closure right
so book in both the cases they are
long-range force let me write down book
the laws that will make things simpler
so if we write down by its separate law
this somewhat like this DB is equal to
MU naught by 4 PI I DL sine theta
divided by R square and in this case
Coulomb's law is F is equal to 1 by 4 PI
epsilon naught Q 1 Q 2 by r square so in
both the cases whenever we talk it is a
long range force that means as it is
inversely proportional to distance as
the distance increases the ache force
decreases here also as the distance
increases the force experienced between
the two charges decreases in my excel
also as the distance increases the
magnetic field experienced is decreases
both of them call the principle of
superposition
that's also correct because if you have
if as I to mentioned earlier also it is
a vector field right so if you have a
system where individual charges produce
some magnetic field B 1 B 2 B 3 and so
on then the net magnetic field of the
system will be the vector sum of the
individual magnetic fields similarly in
this case also in Coulomb's law also
they follow principle of superposition
by its in case of by it's a good law it
is produced by a vector source but in
Coulomb law it is produced by a scalar
source what does the vector source you
think here and what is the scalar source
yet when we talk of Coulomb's law what
is the source the source is nothing but
a charge so Q is the source charge is
the source if there is no charge there
will be no force of attraction or
repulsion right so the origin of
Coulomb's law is the charge but in this
case there is no concept of charge as
such right because in this case then it
is about moving charges it is not about
a single charge if a charge is placed on
the table you will not get a magnetic
field because of that charge it is
because of moving charges so in this
case the sources does ID L that is the
current element it is basically the
current carrying element so a small
element which is carrying some current
that is the source that is the source of
a magnetic field perpendicular to the
displacement vector now in this case
what is the direction when we talk about
the direction of magnetic field if we
talk about direction it has to be mu
naught by 4 pi I DL cross R divided by r
cube in this case if we talk about
direction
that is it would become 1 by 4 PI
epsilon not Q 1 Q 2 R tau divided by r
cube right so that means in this case
the forces along the direction of I but
in this case the direction of the
magnetic field is determined by cross
product of DL and I that means it is
direct it is perpendicular to the plane
containing DL and I perpendicular to the
plane containing this current element
and the position vector right so this
was the comparison of by observer claw
with Coulomb's law thank you please
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