Helical Motion - Moving Charges & Magnetism Video Lecture - Class 12

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now we will discuss some points or some
terminologies related to the helical
motion I mean I told you about the
helical motion but there are certain
terminologies related to the helical
motion which basically defines the
helical motion right so we will discuss
those terms
the first one is radius of the helots so
what is radius of the helix it is
nothing but the radius of the helix
would be nothing but the radius of the
circular path which it
Traverse so it is the radius of the
circular component of motion you
understood right how did we get that
helix the helix is nothing but
combination of the circular motion plus
the linear motion so the radius of that
circular motion is the radius of the
helix so how do we determine the radius
of the helots as I told you that the
magnetic force which acts on the
particle now right now I am talking only
about the circular component of motion
so for the circular component of motion
the magnetic force which acts on the
particle that acts as the centripetal
force right so what is this magnetic
force this magnetic force is nothing but
Q into V cross B now in this case so
this is Q into V cross B and centripetal
force is nothing but MV square by r
where r is the radius of the circular
path now what is V cross V it is nothing
but V B sine theta and what is Theta
theta will be 90 degree because right
now we are talking about the
perpendicular component of velocity so
the velocity is perpendicular to the
magnetic field so this will be Q VB is
equal to mV square divided by r so this
V and B will get cancelled so from this
we can say
that the radius of the helix is equal to
MC divided by QB so this will be the
radius of the LX the next term is the
frequency of rotation
what does frequency of rotation that
means how frequently the charged
particle is rotating that means how many
rotations is it completing per second
that is the frequency right so how can
we find out the frequency of rotation
let us try to do that also we know that
velocity is related to linear velocity
is related to angular velocity this way
that as velocity V is equal to R into
Omega where Omega is the angular
velocity and R is the radius of the
circular path right so from this we can
say that V by R is equal to Omega right
now we have already derived an
expression for R so we can put that so
it becomes MC divided by QB so this
becomes Q B divided by M this is angular
velocity now what is this this is
angular frequency so this angular
velocity can be written as 2 pi nu right
so this is equal to QB divided by M
therefore frequency becomes equal to QB
divided by 2 pi M so this becomes the
frequency of rotation like this this
this term describes how frequently the
charged particle will come complete one
rotation and how many rotations will be
there per second next is the time period
of the circular motion so obviously once
we have found out the frequency of
rotation it is very easy to find out the
time period time period
is nothing but 1 by frequency of
rotation right so this will be equal to
2 pi M divided by QB this is one way of
finding time period also you can find
out time period like this time period is
nothing but the total distance traveled
divided by velocity so what is the total
distance traveled in a circular path
total distance traveled is nothing but
the circumference of the circle which is
2 pi I divided by velocity which is V so
here we put the value of R where R is MV
divided by big cube so here V and we
will get cancelled so you get 2 pi M
divided by QB so you get the same value
for both the cases so this is the time
period time period is nothing but time
taken by the charge to complete one
revolution the fourth term is pitch what
does pitch pitch is the distance moved
along the magnetic field now when you
are covering the circular path at the
same time you are also covering some
distance linearly for example here if
you see the circular motion is there but
at the same time there is some linear
part which is getting covered so this
distance which is covered along the
magnetic field that is called pitch that
means in this case we are considering
the parallel component of velocity so
what is the distance cup distance move
let us denote which with P so the
distance move will be nothing but
velocity into time so velocity in this
case will be the parallel component of
velocity into the time period by time
period which means the distance which is
it has moved while the circular motion
has covered one revolution that means
when one revolution is covered here how
much distance is covered linear right so
this will be the velocity will be
parallel component of velocity and time
taken will be the time period of one
revolution right so this V parallel
multiplied by
two pi M divided by QB
so this becomes the pitch of the helots
so these are the four terms which
describes a particular Phoenix that is
the frequency of rotation radius of the
helots time period of the helix and the
pitch of the hell's so I hope that I am
able to explain you the kind of motion
which a charged particle has when it
enters an external magnetic field thank
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