Magnetic Dipole Moment of a Revolving Electron Video Lecture - NEET

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magnetism part 33 is brought to you by
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please make sure that you have watched
all the videos to the part 32 before
going ahead with this one so now we will
talk about the magnetic dipole moment of
a revolving electron now prom on Bohr's
theory we know that that every atom
consists of a nucleus which is
positively charged and which contains
all the protons and neutrons and it
consists of electrons which are
revolving around the nucleus in some
circular orbit right so let us suppose
this is my nucleus which has a charge of
plus Z II so let us say that charge on
nucleus is plus Z II and this is my
electron which revolves around the
nucleus in somewhat circular path and
the charge on the electron is minus II
now electron moving around the nucleus
this movement of electron is nothing but
movement of charge now moving charges
constitute a current right so that means
electron moving around the nucleus
electron moving around nucleus this
constitutes a current because any moving
charge constitute current so you can
write down that this current is nothing
but charge per unit time so charge is
the charge on an electron per unit time
what is this time time period to
complete one revolution so this time is
the time to complete one revolution so
this time is nothing but the distance
traveled in one revolution that is 2 pi
R that is the circumference of this
circular path divided by the velocity of
the electron
so this B is nothing but the orbital
speed of electron alright so now if you
put this in this expression what do you
get current is equal to e divided by 2
pi R into B so this would be the current
that is constituted due to the movement
of this electron about the nucleus now
let us try to calculate the magnetic
moment of electron so magnetic movement
of electron due to its orbital motion is
generally denoted by mu n this L
subscript is subscript is for the
orbital motion of electron magnetic
moment is nothing but product of current
and area so current into area now
current in this case is e into V divided
by 2 PI R and what is area area is
nothing but PI R square so this pie pie
will get cancelled R and R will get
cancelled so we get e V R divided by 2
so the magnetic moment of electron is
equal to e V R divided by 2 and what
would be the direction of magnetic
moment now in if you look at this figure
what do you see somewhat this is the
part of the electron right and let us
say this is the radius of its path and
suppose we are assuming that the
electron is moving in this direction so
if the electron is moving in this
direction so what would be the direction
of current now if the electron is moving
in this direction so it is constituting
electronic current right now we are
talking about electronic current so if
this is the direction of current your
magnetic field what would be the
direction of your magnetic field
so the direction of your magnetic moment
which is given by current into area so
that magnetic moment will act vertically
downwards so this magnetic moment will
act vertically downwards right so what
would be your magnetic moment now you
can run so now this magnetic moment can
be further written like this
evie are divided by two we multiply the
numerator as still as well as
denominator with mass of electron so
what do we get we get e divided by 2m e
into V into R into M e now what is this
MV and MV R is nothing but the angular
momentum of electron which is equal to e
divided by 2m e into M right this L is
nothing but the magnitude of orbital
angular momentum now don't get worried
with these terms like orbital angular
momentum and stuff like that because I'm
sure you would have studied about all
these things in your chemistry lessons
so what do we conclude we observe that
the orbital magnetic moment of electron
is equal to minus 2 MV into L so this
shows that the magnetic moment of
electron is in a direction opposite to
the angular momentum of electron so this
implies that angular momentum of
electron is opposite in direction to the
magnetic moment of electron so from this
we conclude that any charge in uniform
circular motion would have an Associated
magnetic
so for electron also because of its
orbital motion we have this orbital
magnetic moment so we can get because of
the fact that electron has spins
electron spins about itself there is
another magnetic moment associated with
electron that is known as magnetic
moment due to spin off electron which is
denoted by mu s right so the net
magnetic moment of an electron is given
by vector addition of mu s and mu a so
we will talk about all those things when
we discuss especially about electrons
but for now I just gave an example of
electron you show that any charge which
is a uniform circular motion would have
an Associated magnetic moment because
any charge in circular motion will
constitute current and there will be a
magnetic moment associated with that
current so that is how we reach the end
of this lesson on magnetism so we we
have few more things not only few more
things but a lot more to discuss about
magnetism which we will continue in our
next lesson so for now we will solve
some problems on some of the topics
which we on which we haven't solved
problems put thank you please visit exam
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