Magnetic Force on a Charge Video Lecture | Physics for JEE Main & Advanced

hi it's mr. Andersen and this is ap
physics essentials video 31 it's on the
magnetic force imagine we have a charged
particle like a proton moving through
space since there's no force acting on
it no field acting on it it's just going
to keep going in that direction but if
we have a charged particle that's moving
by a magnetic field like it's rushing
from the Sun and it's coming by the
earth and the earth acts as a big magnet
what it's going to do is it's going to
apply a force to that and it's going to
spiral into the planet and it causes the
Northern Lights as these protons and
electrons hit in our atmosphere we're
giving off ionization colors and so as
we move into magnetic forces we really
are moving into a third dimension and so
we have to have a way to deal with that
so if we have just two dimensions it's
easy to do that on a piece of paper but
how do you do it with three dimensions a
magnetic field for example coming at you
or going away from you the way I
remember it is it's like an arrow if an
arrow is going through a hole you're
just going to see that point on the end
and so if you see concentric circles
like that or a bunch of them that means
the magnetic field is coming towards you
and then the tail end of the arrow is
going to look like that and so if we see
a plus sign or X inside the circle that
means that it's going away from us and
that'll make sense when you see diagrams
like this so we've got a magnetic field
you can see that's coming out at us and
let's say we have a charged particle
that has no velocity it's just sitting
there is there a magnetic force acting
on that charged particle the answer is
no if it's not moving there's no
magnetic force but as it moves it has a
velocity vector and if you're ever
moving as a charged particle through a
magnetic field then you're going to have
a force applied to you and we call that
the magnetic force or F sub n now things
that you need to remember is that it's a
perpendicular line between the magnetic
force and the velocity and it's also
perpendicular between the magnetic force
and the magnetic field but the velocity
vector in the magnetic field vector
don't have to be perpendicular to each
other how do we calculate the magnetic
force well there are only three things
that really deal with that first one is
going to be Q that's going to be the
charge of that particle in this case it
would
just be the elementary charge we then
have the velocity vector or the speed of
the particle and then we're going to
cross product that with the magnetic
field and what's a cross product well
these two vectors when we when we
multiply those together we're going to
get a third vector that's going to move
in a different dimension
I got an animation that's going to show
you that now depending on that angle we
can get different amounts of this
magnetic force and so we use sine theta
to figure out how much that's going to
vary over time and so let's say we have
a magnetic field like this you can see
that it is coming at us to figure out
where that magnetic force is acting you
have to use the right hand rule and so
it takes a second to get this figured
out but I'm going to hold my fingers out
like this so I've got my index finger
pointed out that's going to be the
vector of the velocity so in other words
where that charged particle is moving I
then have my middle finger moving at 90
degrees to that and that's going to be
the magnetic field and then the force is
going to be your thumb and so you try to
make these three dimensions with your
finger and you can solve really intense
problems like this you might look like
an idiot as you're doing that but it's
it's worth it so let's say we have a
charged particle that has no velocity
and it's in this magnetic field how big
is our force going to be well we're not
going to have a force again if it's not
moving there's no force and so let me
give you a harder problem let's say we
have a magnetic field like this and we
have a charged particle a positive
particle that's moving up into the left
and so how do you figure out where that
magnetic force is going to be well first
of all make your hand like this and then
you're going to point your index finger
in the direction of that moving charge
so I'm moving it up and to the left then
you want to make sure that your middle
finger that magnetic field is pointed
towards you because you can see on this
diagram that the field is coming towards
us and so once I've got that in order my
thumb is going to show me the magnetic
force and so that's going to go up and
to the right so that was pretty easy to
solve let's go to another one now we've
got a different magnetic field and let's
say that that charged particle that
proton is moving from right to left how
do you solve this one again
stick your finger towards the left
that's the movement of the particle now
the magnetic field is not coming towards
you it's going away from you so I have
to
turn my hand like this and now where's
the magnetic force well you can see that
that's going to be acting down what if
we have one like this so we've got a
different magnetic field what if we have
an electron moving okay so if you have
an electron moving there's two ways you
can go at this number one you could just
use your right hand and then just turn
the force around when you're done or
you've got a left hand and the left hand
is going to work great so I'm going to
put my finger point my index finger in
the direction of the movement of the
electron the magnetic field my middle
finger in this case is going to come at
me and so where's the force now the
force is going to be to the left and so
if you know the magnetic field and you
know the direction you can always figure
out where that magnetic force is going
to be now the angle as I said is between
the velocity and the magnetic field is
not always 90 degrees and so we call
that theta and depending on what that is
we're going to get a different amount of
that magnetic force and so those two are
perpendicular but the third one is not
going to be perpendicular and so here's
our equation it's a little scary but
it's not that bad
q is going to be the charge V is going
to be the velocity and then this is a
cross-product between the two and so
let's watch the animation before we get
to the sine of theta and so if they're
pointed in the same direction velocity
and magnetic field we have no force but
watch what happens when they become
perpendicular we have a greater force or
magnetic force if it moves to 180
degrees what's our magnetic force at
this point it's going to be zero as I
move it back to 90 degrees then it's
going to be at its maximum at this time
and so by using this sine theta in the
middle we can figure out how much this
cross-product or in other words
multiplying the velocity times the
magnetic field is affecting the overall
magnetic force and so the parts of this
formula are Q which is charged measured
in coulombs V is going to be the vector
velocity that's going to be in meters
per second and then we have B which is
going to be our magnetic field and we
measure that in Tesla's and then as we
solve for the magnetic force that's
going to be measured in Newtons and so
let's get to that theta in the sine of
theta where's that coming from
well let's say that our magnetic field
and our velocity are perpendicular to
each other we know that that's going to
be the maximum amount of magnetic force
that we can get what if it's this
direction they're in opposite directions
you remember what our
our magnetic force is going to be here
it's zero and if they're if they're both
moving the same direction it's also
going to be at zero and so if we just
choose that angle to be theta and then
we have sine of theta
look what numbers we're going to get so
if it's a zero degree angle sine of zero
is going to be zero there's going to be
no magnetic force likewise sine of 180
is going to be zero but if we're at
ninety degrees that's going to be one
and the AP folks say that you should
really understand zero nine degrees 90
degrees and 180 but the sine makes sense
to me and it should make sense to you as
well what's our angle look like right
here well that's around a 45 degree
angle so what's the sine of 45 it's just
going to be 0.7 zero
it's going to be somewhere between one
and zero and so if we do a problem like
this calculate the magnetic force acting
on a proton traveling at three point
zero times ten to the fifth meters per
second perpendicular to 0.32 Tesla
magnetic field
how could you figure out the magnetic
force well you just start with your
equation Q V sine theta of B what do I
know well I know the magnetic field
that's 0.32 Tesla's I know the velocity
three point zero times ten to the fifth
I know what the sine of theta is going
to be because that's a 90-degree angle
so that's going to be one the only thing
I don't have it seems like is Q that's
going to be the elementary charge so we
just write that out like this and then
we solve and we're going to have a
really small force that's acting on that
charged particle in that proton and so
did you learn to apply mathematical
routines to express the force exerted on
a moving charge particle in a magnetic
field always use your right hand and
you'll probably need to calculate it to
do the rest and I hope that was helpful