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# Magnetic force on a charge

## Video transcript

we know a little bit about magnets now let's see if we can study it further and learn a little bit about magnetic field and actually the effects that they have on moving charges and that's actually really how we define magnetic fields so first of all with any field it's there's good it's good to have a way to visualize it with the with the electrostatic fields we drew a field line so let's try to do the same thing with magnetic field so let's say this is my bar magnet this is the North Pole and this is the South Pole now the convention when we're drawing magnetic field lines is to always start at the North Pole and go towards the South Pole and you can almost view it as the path that a magnetic north monopole would take so if it starts here from magnetic north monopole even though as far as we know they don't exist in nature although they theoretically could but let's just say for the sake of argument that we do have a magnetic north monopole if it started out here it would want to run away from this North Pole and would try to get to the South Pole so it would do something its path would look something like this and if it started here maybe its path would look something like this or if it started here maybe its path would look something like this I think you get the point another way to visualize it is instead of thinking about a magnetic north monopole in the path it would take you could think of what what if I had a little bit of a little compass here let's say let me draw it in a different color let's say I put the compass here field and that's not where I wanted to do it let's say I do it here the compass pointer will actually be tangent to the field line so the pointer could look something like this at this point it would look something like this and this would be the North Pole of the pointer and this would be the South Pole of the pointer or you could you know that's how North and South were defined people had compasses they said oh this is the North seeking Pole and it points in that direction but it's actually seeking the South Pole of the larger magnet and that's where we got into that big confusing discussion of that the the magnetic geographic north all that we're nor used to is actually the South Pole of the magnet that we call earth and you could view the last video on introduction to magnetism to to get confused about that but I think you see what I'm saying North always seeks out the same way that positive seeks negative and vice-versa and North runs away from north and really the main conceptual difference although they are kind of very different properties although we will see later they actually end up being the same thing that we have something called an electromagnetic force once we start learning about Maxwell's equations and relativity and all that but we don't worry about that right now but in classical electricity and magnetism they're they're kind of a different force and the main difference although you know this field lines you can kind of view them as being similar is that magnetic forces always come in dipoles while you could have electrostatic forces that are multiples you could have just a positive or a negative charge so that's fine you say Sal that's nice you drew these field lines and you've probably seen it before if you ever dropped metal filings on top of a magnet they kind of arrange themselves along these field lines but you might say well that's kind of useful but how do we determine the magnitude of an elected a magnetic field at any point and this is where it gets interesting the magnitude of a magnetic field is really determined or it's really defined in in terms of the effect that it has on a moving charge so this is interesting I've kind of been telling you that we have this different force called magnetism that is different than the electrostatic force but we're defining magnetism in terms of the effect that it has on a moving charge and that's a bit of a clue and we'll learn later or hopefully you'll learn later as you advance in physics that magnetic force or a magnetic field is nothing but an electrostatic field moving at a very high speed at a relativistic speed or you could almost view it as they are the same thing just from different frames of reference I don't want to confuse you right now but anyway back to what I'll call the basic physics so if I define a magnetic field as B so B is a vector and it's a magnetic field we know that the force on a moving charge could be an electron on a proton or some other type of moving charged particle and actually this is the basis of how they you know when you have super colliders how they get the particles to go in circles and how they studied them by based on how they get deflected by the magnetic field but anyway the force on a charge is equal to the magnitude of the charge of course this could be positive or negative times and this is where it gets interesting the velocity of the charge cross the magnetic field so you take the velocity of the charge you can either multiply it by the scalar first or you can take the cross-product then multiply it by the scalar doesn't matter because this is just a number this isn't a vector but you essentially take the cross product of the velocity and the magnetic field multiply that times a charge and then you get the force vector on that particle now there's something that should immediately if you hopefully get a little bit of intuition about what the cross product was there's something interesting going on here the cross product it cares about the vectors that are perpendicular to each other so for example if the velocity is exactly perpendicular to the magnetic field then we'll actually get a number if they're parallel then the magnetic field has no impact on on the charge so that's one one kind of interesting thing and then the other interesting thing is when you take the cross product of two vectors the the the result is perpendicular to both of these vectors so that's interesting a magnetic field in order to have an effect on a volt on a charge has to be perpendicular to its velocity and then the force on it is going to be perpendicular to both the velocity of the charge and the magnetic field I know I'm confusing you at this point so let's let's play around with it and do some problems but before that let's figure out what the units of the magnetic field are so we know that the cross product is the same thing as so let's say what's the magnitude of the force the magnitude of the force and I'm going to arbitrarily change colors is equal to well the magnitude of the charge is just a scalar quantity so it's still just the charge times the magnitude of the velocity times the magnitude of the field times sine of the angle between them this is the definition of cross-product then we could put you know if we wanted the actual force vector we could just multiply this times the vector we get using the right hand rule we'll do that in a second but anyway we're just focused on units sine of theta has no units so we can ignore it for this discussion we're just trying to figure out the units of the magnetic field so force is Newton's so we could say Newton's equals charges coulombs velocity is meters per second and then this is times the the I don't know what we'll call this the B units we call them units sub B so let's see if we divide both sides by coulombs and meters per second we get Newton's per Coulomb and then if we divide by meters per second that's the same thing as multiplying by seconds per meter equals the magnetic field units so the magnetic field in SI terms is defined as Newton seconds per Coulomb meter and that might seem a little disjointed and they've come up with a brilliant name and it's named after deserving fellow and that's Nikolai Tesla and so the one Newton second per Coulomb meter is equal to one Tesla and and I'm actually running out of time in this video because I want to do a whole problem here but I just want to sit and think about it for a second even though you know in life we're used to dealing with magnets as you know we have these magnets and they're they're fundamentally may be different than what at least we imagine electricity to be but the magnitude of or actually the units of magnetism is actually defined in terms of the effect that it would have on a moving charge and that's why the unit 1 Tesla or a Tesla is defined as an Newton second per Coulomb so the electrostatic charge per Coulomb meter well I'll leave you now in this video maybe you can sit and ponder that but it'll make a little bit more sense when we do some actual prop with some actual numbers in the next video see you soon