Circular current loop as magnetic dipole - Moving Charges & Magnetism Video Lecture - Class 12

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going ahead with this one now we will
look at the circular current loop as
magnetic dipole like how we study about
electric dipole in case of
electrostatics
similarly we will talk about something
called magnetic dipole so in case of
magnetism also we have something called
in magnetic dipole but in magnetism a
current a circular current loop acts as
a magnetic dipole so I mean this is
quite strange for you right because in
case of when you talk about electric
dipole it is basically a system of two
charges of equal magnitude but opposite
sign separated by some distance that was
known as electric dipole so you will be
expecting something of that sort in case
of magnetic dipole also but when we talk
about magnetism there we do not have
anything like magnetic monopoles or
magnetic charges so in magnetism we
considered the all it is found actually
that a circular current carrying loop
acts as a magnetic dipole so here I will
quickly tell you I will quickly show you
certain evidences which will tell that
yes a magnet a circular current carrying
loop can be considered as a magnetic
dipole now we know that what is the
magnetic field on the axis of a
current-carrying circular current
carrying loop let us suppose if this is
a loop which is carrying some current I
and if you want to calculate the
magnetic field at some point P so what
and we we see that the radius of this
coil is odd and this point P is located
at some distance X so magnetic field on
axis of circular current loop we have
already derived this night in this
lesson itself sometime back so that is
given by mu knot I R square divided by 2
into R square plus X square to the power
3 by 2 right where X is the position of
the point where we want to calculate the
magnetic field and R is the radius of
the circular loop right now if we assume
that X is very very greater than R that
means if we want to find out the
magnetic field at a point which is far
away from this circular loop in that
case we can write this as mu knot IR
square divided by 2 into X s cube right
because we can ignore R square as R is
very small when compared to X now here
we know that the area of this loop is
equal to pie R square right so if we
want we can write R square as ay by I so
this will become u knot i.e by pie right
now what is current into area
current into area is nothing but
magnetic moment so this is mu knot M
divided by 2 Pie X s cube so what do you
get so this V becomes now if you
multiply 2 to the numerator as well as
denominator you get mu naught by 4 pie
into 2 m by X s cube so this is your
magnetic field at a far axial point for
a circular current loop now compare this
expression with the expression which you
get in olestra statics so let us try to
replace new knot with 1 by epsilon not M
that is magnetic moment with dipole
moment and magnetic field with electric
field so if you replace these things
what do you get you get electric field
he is equal to 1 by 4 pie epsilon-not to
be divided by XS 2 and what is this this
is the electric field at an axial point
of electric dipole right and I told you
before also electrostatics and magnetism
magnetism they share a very good
analogic so everything is analogous so
here the expression for magnetic field
which you found for an axial point of a
circular current carrying loop if you
replace the corresponding parameters of
electrostatics and that you get an
expression of electric field which is
the electric field at an axial point of
electric dipole so you can see that this
is nothing but the magnetic field at an
axial point of magnetic dipole so
magnetic dipole is nothing but your
circular current that current loop so
you can see that your search inner
current loop acts as a magnetic dipole
so when we talk about magnetism magnetic
dipole is nothing but a circular
currently now you must be thinking that
at the end of this chapter I am talking
about some small small things and bits
and pieces
that's because when we go ahead with our
next lesson that is matter and magnetism
you will find the usage of all these
things so now the conclusion for this
was that a planar current loop is
equivalent to a magnetic dipole of
dipole moment M is equal to I into named
at large distances see this large
distances has an important role to play
because since we considered large
distance that is why we can see that
that X is very very greater than I and
that is how we derive that expression
which is similar to the expression for
electrostatics right ok so now let us
compare the magnetic dipole with our
electric dipole when we think of our
electric dipole it consists of two
charges when we talk of magnetic dipole
it
consists of the current loop in electric
dipole electric monopole exist what do I
mean by monopole monopoles means a
charge cube for example in electrostatic
a dipole would mean plus Q minus Q
separated by some distance to it right
so in electric dipole each of these
charges actually exist
so each of these is called mono poles
these two together two poles together
form a dipole that is two poles so that
means mono poles actually exist each of
them actually exists but in case of a
magnetic dipole it is nothing but a
current loop so we cannot separate the
two poles of this magnetic dipole
however it behaves like a magnetic
dipole but you cannot the two we cannot
separate the two mono holes so we say
that magnetic monopoles do not exist
then we study the lesson on mapping and
magnetism you will see that when we
study more about magnetism you will get
to know that there are so many other
evidences which prove that magnetic
monopoles do not exist at all thank you
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