in this video we introduced the lorentz force law describing the direction and magnitude of
the magnetic force exerted on a charged particle moving through a magnetic field we follow up with
a series of qualitative questions on the direction of magnetic force and we're going to cover
quantitative questions in several other videos and i'll just post links to those when they're ready
so in the picture on the left i have a magnetic field pointing up i have a charged particle with a
positive charge moving through that magnetic field at some angle with respect to the magnetic field
looks like it's in the neighborhood of 45 degrees and there's my velocity vector and my speed would
be v so it turns out the magnetic force is given by this lorentz force law the magnetic force
is proportional to the size of the charge interestingly enough it's proportional to
the speed itself so if you double the speed of the particle the force doubles
and of course the force is proportional to the strength of the magnetic field
and then it has this sine theta term in it and what this does is it means that the magnetic
force is going to be zero if the velocity is parallel to the magnetic field because that
would make this angle zero and it's going to be maximized if the angle is 90 degrees
for those of you with a little more calculus or physics experience
you might prefer to write this as a cross product and that cross product actually has the direction
of the magnetic force folded into it in this video we're going to talk about how to get the direction
of the magnetic force using what are called right hand rules and i've shown three different methods
here it's not really clear what's going on in each one until i really explain it but there
are three different relatively popular ways of figuring out the direction of magnetic force
so in each case strangely enough the magnetic force is perpendicular to both the velocity
and the magnetic field and then you have to figure out exactly which way it points um in our original
picture here the only way to be perpendicular to both the magnetic field and the velocity is for
the force to either be pointing out of the page or into the page and the right hand rule is designed
to help you make that decision i'll call the first one method one and in method one you think of your
fingers as the magnetic field lines i tried to get my fingers to point straight up but i guess
they're kind of crooked you let your thumb point in the direction of the velocity vector and when
you orient your hand in this way the magnetic force is going to point straight out of your palm
which means the answer here is that the magnetic force is pointing out of the page
this introduces a complication because the magnetic force is so truly three-dimensional
we need a new notation for vectors that point in and out of the page so real quick this is
what the notation is if you see a dot with a circle around it that means out of the page
and that's supposed to represent the tip of the arrow because after all vectors are arrows
if you see an x with a circle around it that's into the page and that represents the tail
feathers of the arrow so our answer using method one here is that the magnetic force
is pointing out of our palm and out of the page in method number two and this
is the one that seems to be the most popular in textbooks but it's just not the way i learned it
so i don't really use it very often you take your index finger and let that point in the direction
of the velocity vector your middle finger points in the direction of the magnetic field
and in order to line your hand up this way you've got to make a choice on how your thumb is oriented
and the orientation of your thumb gives you the direction of the magnetic force
and it's the same answer my thumb is pointed up here i'll just put the force vector on
the tip of my thumb now method number three is the one that i actually use in practice
and i think it's because it's more the way that you visualize a cross product in multi-variable
calculus that's probably how it started and it's very similar to method two it's just that
instead of putting your index finger one way your middle finger the other you treat it as a motion
so i orient my fingers in the direction of the velocity and then i sweep my fingers out in an
inward motion so in the palm more direction until they line up with b and the only way to rotate my
hand that way is to have my thumb oriented in the correct direction for the force so this
one involves motion which makes it a little more complicated to deal with in a video again i get an
outward force out of my thumb and i'll just roll a clip real quick to illustrate how the motion works
okay let's get into our examples in example a i have a magnetic field pointing to the left
i have the velocity of a charged particle pointing up now you can take your choice of
these three methods the one i'm usually going to show is method three because that's the way
i'm most comfortable doing it so what i do is figure out how can i align my fingers in the
direction of v and sweep out to the direction of b through an angle less than 180 degrees if
you try to do this the wrong way you're going to sprain your wrist and so the clip looks like this
and the only way to get it done was to have my thumb sticking out of the page
so that's the direction of the force vector in example b i have a magnetic field into
the page and a velocity to the right i figure out how to orient my right hand so i can sweep
my fingers out from the direction of v to the direction of b without spraining my wrist
and the only way to do that is for my thumb to be pointing upward so there's the direction of
the force again again i encourage you to check out these other methods too like for
example i could put my fingers pointing into the page for the magnetic field lines my thumb
pointing to the right and then my palm would point straight upward i get the same answer
c is exactly the same as b except i switched it to a negative charge so remember the rule is if
the charge is negative you just get the opposite result for the magnetic force and then finally in
part d i have a velocity at some angle and i have a magnetic field that's pointing out of the page
so i try to orient my hand in a way that allows me to sweep out with my fingers in the direction of v
to the direction of b so my finger is pointing up and to the right and then sweeping out of the page
and that gives me a magnetic force in this direction now again the right hand rules
they give you pretty much the right direction but you're not going to orient your hand perfectly you
can perfect your answer by remembering that the magnetic force is always going to be perpendicular
to the velocity vector and the magnetic field lines
if you find the physics content on zack's lab helpful click on the zackslab logo on
the right to browse playlists and subscribe to the channel i produce over 100 new videos per
month and subscribing is the easiest way to find new content thanks for watching