Motion of Charged Particle in Magnetic Field Video Lecture | Physics for JEE Main & Advanced

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going ahead with part 9 now we will
study about the motion of a charged
particle in magnetic field till now we
saw that when a charged particle enters
a magnetic field what is the for static
experiences now you can see what today
the kind of motion or what will be the
nature of path that the charged particle
will follow once it enters a magnetic
field so let us do let us try to find
that out so for that we make two
assumptions the first is that we assume
that the magnetic field is uniform that
means the magnetic field the magnitude
of the magnetic field is same throughout
the strength of the magnetic field is
same throughout and the second is the
magnetic field is perpendicular down the
plane of the paper we assume that the
magnetic field is in the downward
direction
I hope you understood what - what do I
need when I say it is in the downward
direction that means it is perpendicular
to the plane of your paper and it is
towards the downward direction so we
will represent it by a cross right so
now we will try to look at the motion of
the charged particle now what can I
decide the motion of a charged particle
obviously the velocity of the charged
particles the velocity of the charged
particle can give us a few that how will
the particle move right now the velocity
of the particle let us suppose that the
velocity of the particle is V so now
this velocity will have two components I
mean any particle which is moving with
some velocity V that we will have two
components one is the perpendicular
component and another one is the
parallel component so here also the
particle I assume has it it does the
magnetic field it has some velocity V
with respect to the magnetic field let
us suppose that there is a parallel
opponent and there is a perpendicular
component so we will consider the motion
of the particle first due to the
perpendicular component then we will see
the motion of the particle due to the
parallel component and then we will try
to join both of them and see how the
motion the overall motion of the
particle will be so let us first
consider the perpendicular component of
the charged particle now let we are
considering the perpendicular component
first okay so now when V is
perpendicular to velocity in this case
the velocity is perpendicular to the
magnetic field so magnetic field is in
the downward direction this cross shows
that this is the direction of magnetic
field now let us suppose that the
charged particle is at this point is at
some point if this particle has just
entered and the particle is at this
point the velocity of the particle is in
this direction the particle wants to
move in this direction and the magnetic
field is downwards now I apply your
right hand rule so if you apply a right
hand rule your fingers will go towards
velocity and then it will curl down so
your force will be towards this
direction that means if you take your
fingers all your four fingers will be in
this direction that is the direction of
velocity then they will curl down so
when you curl your fingers down where is
your thumb your thumb will point in this
direction like so this is the direction
of the force
now this charged particle so force is in
this direction so that particle wants to
go in this direction but since the force
is in this direction it will push the
particle towards this direction now
again this particle goes to some point
and again if you consider this point
later suppose now the particle came to
this point here again what will be the
velocity of the particle the velocity
will be in this direction magnetic field
is downward again you apply your right
hand rule your force will be towards
this direction so again that force will
bring the particle here so if you see
that the force will always act inwards
and because of this force the particle
end up following a circular path are you
understanding the logic by the particle
is experiencing up I mean it will move
in a circular path because the force
which is acting on the particle force
that is the magnetic force what does
this force magnetic force the force
which is acting on the particle as soon
as it enters the magnetic field so the
magnetic force is always acting on the
particle inwards so it is pushed I am
trying to bring the particle inward but
the particle has some velocity which is
tangential so as a result of this this
magnetic force acts as a centripetal
force and this particle is moving in a
circular motion so that means this is
the result of the perpendicular
component so this came from the
perpendicular component of velocity the
component of velocity which is
perpendicular with respect to the
magnetic field but there is another
component that is the parallel component
now for the parallel component of
velocity what will happen now when V is
parallel to B in that case the magnetic
force on the particle will be zero right
in this case see in this case the
magnetic force that is F is equal to Q
into V cross B so it was nonzero right
but in this case the magnetic force will
be equal to zero by so because it is V
cross B that is V B sine theta and theta
will be equal to zero because V is
parallel to B so the magnetic force in
this case is zero now what will happen
if the magnetic force is zero that means
if the particle is end let us suppose if
this is the particle and if this
particle enters into a magnetic field
let us suppose this is the magnetic
field again and it is suppose this
charged particle enters into the
magnetic field now this charged particle
will not experience any force due to
this magnetic field because magnetic
force is zero so whatever is the
velocity of the particle that velocity
will remain unaffected so that means if
the particle is entering in this
direction with some velocity V so it
move with that velocity V so what is the
motion nature of the path it is linear
so for the perpendicular component of
velocity the motion is circular because
the mag because there is a magnetic
force which will act on the particle and
that magnetic force will act as a
centripetal force so in this case this
magnetic force will act as a centripetal
force but in case of the parallel
component of velocity the magnetic force
that will act on the charged particle
will be zero because of which the
velocity of the Partridge particle will
remain unaffected and the particle will
move in a linear time so what do we say
with perpendicular component the motion
is calculate and with parallel component
the motion is linear but in reality both
this components exist together like I
mean any velocity when a charged
particle is moving with any velocity
that velocity will have a perpendicular
component as well as a parallel
component so that means this circular
motion will be there as well as the
linear motion will also be there so what
will be the resultant motion so the
resultant motion of the particle will be
helical do you know what is helical
helical is something like this this is
known as a helical motion that means it
is moving in a circular path as well as
it is moving in a linear path so
circular path you can see clearly and
linear path is this path which it is
covering so the circular motion plus
linear motion gives rise to helical
motion if you look at this you like the
standard better for example here it is
moving in a cycle let us suppose it
moved in a circular path like this and
the same particle moved along a straight
line path like this so when you combine
both of this so in the first case it
moved in a circular path like this in
the second case it moves in this
direction so if you combine both of them
in that case it will move in a circular
path as well as it will keep moving
along this path that means it is moving
along the linear path is also covered
and
circular path was also covered therefore
the resultant motion would be somewhat
like this and this is known as a helical
motion so that means now the concepts
are getting clear at like right so what
is happening you have so let me give you
it quickly just listen to it as a story
you have a wire which is carrying
current that means charges are in motion
so when charges are in motion they will
produce a magnetic field around itself
right now there is a current charge
particle q who is an outsider that
charge particle comes and enters this
magnetic field what happens that charged
particle experiences a force due to this
magnetic field now what will be that
force that the magnetic force is given
by Q into V cross B like now because of
this magnetic force that charged
particle will move in a helical path
right
okay so till now it is thank you
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