If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

Main content
Current time:0:00Total duration:10:36

Video transcript

let's say we have a magnetic field that's coming out of the bright side of the screen and it's it's not just along the screen it's actually you know it's three-dimensional and so it's it's going above the screen below but it the the direction of the magnetic field is from the right to the left let me just draw that and I'm not going to do it I'm not going to draw a bunch of the field vector arrows because that'll just take up a lot of valuable space on our so that's the vector magnetic field that's down here too if I could I would draw it above above your screen and below your screen but is coming from the right to the left and then in that magnetic field I have an electric circuit and I won't draw the whole circuit right now do that in a second but let's say I have part of the electric circuit is a loop and the loop looks like this I'm trying to draw it carefully so that we can because I think a careful drawing will be more useful in a second than an uncaring drawing let's see so it's a loop you can almost you can imagine taking a paperclip and putting it into this shape oh that's good enough I think and I have a current going in this direction in this paperclip so this is the positive that's the negative so the current is going like that current current is going in a loop like that the currents coming out of this end it's coming in to this end so my and let's say that this this loop of it could be a paperclip or anything let's say that it can rotate and that's important what's going to happen well my magnetic field is coming in this direction the current is going down here up here what's going to be the net force on the magnetic of the magnetic field on on the sloop well let's try it out and it turns out is going to be a different magnitude at different points of the current so here and we don't worry about all we're worried about right now is direction and then maybe need a little intuition of the magnitude so we know that the force a magnetic field is equal to the current times cause a length vector cross the magnetic field right well what would be what would be the force of the magnetic field on this segment of wire we could call this L right and that L goes in the same direction as the current let's see current is just a scalar but L is going down magnetic field is going to the left cross product cross product I take my right hand put my index finger I put my index finger in the direction of the of the current or in the direction of L because that's the first term in the cross product that's the index finger so my index finger goes down because that's the direction of the current and then my middle finger and remember you have to do this with the right hand if you do that the left-hander getting out the opposite result and now my middle finger is going to go in the direction of the field so let me point my middle finger my middle finger is going to go in the direction of the field I keep having to look at my own hand and then my other two fingers are just going to do what they need to do so that's my third finger and that's my pinky and then what is my thumb going to do what is my thumb going to do well my hand that's my hand this is kind of this is what my hand is doing I'm pointing downward right and my palm is kind of pointing at my body so what is my thumb doing if I know it's hard to see this is this is my middle finger right here so my thumb is on the other side of this drawing and my thumb is pointing downwards I hope you see that all right and you try it with your own hand so my thumb is pointing downward so the direction of the force created by the magnetic field on this current is going to go downward so let me draw that so the force vector then I'll do it in this orange e brown color the force vector on this segment of the wire is going to be going down now what about this segment of the wire well think about it this segment of the wire the L vector this L vector it's going it's going well it's parallel to the magnetic field just in the opposite direction and so when you take the cross-product if you remember the cross-product is you're multiplying the magnitudes of the vectors that are perpendicular to each other but if this is the L vector right here there's no component of it that it's perpendicular to the magnetic field so the magnetic field and then the current will are in the same plane they're parallel they're not orthogonal at all there's no components of them that are at 90 degrees so when you take the cross-product you're going to see that the net force on this segment of the wire is zero and likewise on this segment of the wire and this segment of the wire because they aren't in any way perpendicular no components of them are even perpendicular so fair enough so all we know right now is a magnetic field is exerting a net downward force on this side of our paperclip or of our circuit now what about this side well same thing take the cross-product if this is our L L cross B so take your index finger in the direction so index finger goes like that your middle finger will go in the direction of the field so your middle finger is going to look something like that and then your other two fingers are going to be like that and where's your thumb going to do and this is has to be a right hand to work your thumb is going to point straight up this is like the heel of your thumb and your thumb is going to I don't know if that's a good drawing of a thumb but your thumb is essentially pointing out of the page right middle finger in the direction of the current or in the direction of our length oh sorry index finger in the direction of current middle finger in the direction of the field thumb points out of the page and do that with your own right hand and you'll see that the net force of the magnetic field on this segment of wire is going to be upwards upwards let me do it in a different color just to get some contrast going to be upwards so what's going to happen assuming that this circuit can rotate what's going to happen on this side where there's a downward force on this side there's an upward force so the magnetic field is actually exerting a torque on this wire right it's exerting a 4 like if you if you viewed if you view this little dotted line as our axis of rotation the whole coil is actually going to rotate around that line and so there's some force over here along the whole line being applied downwards so and it's actually perpendicular to our moment arm if you remember what we had learned about torque so it will actually exert all of that force will be a you know that force times this distance will be the torque applied on this side and then likewise there's an up there's a torque in the it's really the same sign in the same direction because here on the other side of the arm it's pushing upwards so they're not going to cancel out they're both going to reinforce and the this whole coil is going to be turning in this direction right here it's going to be moving up out of your video screen here it's going to be moving down into your video screen now what happens so the I'm going to try to not run out of time either so it's going to start rotating so the left hand side is going to go below the page the right hand side is going to be above the page I want to draw some perspective that's why I'm just drawing it bigger so maybe it looks like that maybe the my circuit starts to look like that and I'll redraw my axis of rotation so this is my axis of rotation another way I drew it this part of the axis of rotation is still in the plane of our video but this part of the coil is you can imagine it popping out I wish you had 3d glasses on it's popping out of your screen this part is going into your screen right and the current is still going in the same direction current is going in that direction they're going in that direction there so using the same right-hand rule on this side of the wire the magnetic field is going to be exerting a net downward force but the torque is actually going to be less right because our actual arm moment arm distance is going to be like I want to draw it with some perspective it's going to look something like that right so it's going to be going to the left and behind the page while the torque is still just into the page so you would actually take the component of the torque that's perpendicular so there's some component the torque that's actually perpendicular I don't to confuse you too much but you could imagine the the torque lessens even though the net magnetic force is the same the component of that force is perpendicular that's perpendicular to your moment arm that lessens so there's still going to be some torque that's going to be causing it to rotate downwards in that direction and sorry you know what I drew this wrong here right we're pushing up on the right hand side we're pushing down on the left hand side so the direction is going to be like that right pushing up on the right hand down on the left hand so you're still going to be doing the same thing here you're going to be pushing up here we're going to be pushing up directly out of the page directly out of the page but that's not completely perpendicular to the to the moment arm so some so the component that is perpendicular it's actually creating rotational torque that's going to be a little less and then you can imagine that all the way to the point the coil is going to keep rotating at a smaller width smaller torque and at some point you'll be looking at it head-on so I can just draw it like a straight line right you can imagine this arm is on top and this arm is behind it and at this point what's going to happen all of the magnetic force on this top arm is going to be popping up right it's going to be popping up out of your page but it's not going to be providing any torque because it's not perpendicular anymore to the to your moment arm and likewise on the bottom on the bottom behind this if you could visualize this it would be exerting a net downward force and that's also not going to be helpful but maybe there has some angular momentum so the the wire will still rotate but then when it still rotates what's going to happen and this is where I'll leave you with a little bit of a conundrum actually I don't want to go over the YouTube limit so I'm going to continue this in the next video and I'll show you the conundrum see you soon
AP® is a registered trademark of the College Board, which has not reviewed this resource.