19.1 Introduction to Magnetic Fields and Magnetic Forces

an introduction to magnetic fields and forces going to be the topic of this lesson in my new General Physics playlist which when complete will cover a full year of University algebra based physics now in this lesson we're going to start by taking a look at a simple bar magnet we'll use that to introduce magnetic field to kind of Trace them and we'll see some similarities to the electric dipole we saw in the last chapter and then we're going to take a look at the magnetic force acting on a charge in Motion in the associated calculations my name is Chad and welcome to Chad's prep where my goal is to take the stress out of learning science now if you're new to the channel we've got comprehensive playlists for General chemistry organic chemistry General Physics and high school chemistry and on Chads prep.com you'll find premium Master courses for the same that include study guides and a ton of practice you'll also find comprehensive prep courses for the DAT the MCAT and the oat so we're going to start this lesson off by taking a look at the magnetic field lines around a simple bar magnet like this one and every bar magnet is what we call a magnetic dipole it has two poles every time you've got a Magnetic North Pole and a magnetic South Pole those are the labels we give to them they're kind of opposite poles if you will uh and it turns out even if I cut this magnet in half and create two smaller pieces each of those pieces will also have a magnetic north and a magnetic South and if I cut those pieces in half each of the new pieces will have a magnetic north and a magnetic South and you can keep going on so it turns out that every bar magnet is going to have a magnetic north and a magnetic South Pole every time now in drawing the magnetic field lines it's uh instructive to go back and remind ourselves of what the electric field lines look like with an electric dipole Now with an electric dipole it's a little bit different because we actually we actually have separate point charges where with our bar magnet here it's one piece of metal or fom magnetic materials the case may be that has a north and a South Pole built into that single piece of metal but you might remind yourself an AIA question all electric field lines originate where and terminate where where well they all originate either on a positive charge or from infinity and terminate either on a negative charge or at Infinity so in this case with the electric dipole the electric field lines always go from positive to negative and we're going to find that the magnetic field lines around a bar magnet look very similar and they always go from north to south sort of as we'll see so it's going to look very similar here though but we're going to start with North and work our way around to South same thing around the other side here and we can make bigger field lines just like we did with the electric dipole as well and now we're going to see the one exception though is that there's actually uh electric I'm sorry there's actually magnetic field lines going right through the bar magnet as well but from south to North so here's where we got to be careful if we said you know where do the electric field lines run in an electric dipole well always from positive negative period no exceptions but if we said where do the magnetic field lines run around a bar magnet so as long as we're talking around the bar magnet outside of the magnet it's from north to south but if we talk about through the magnet itself it's from south to North and so we got to be careful one how we ask that question but two how you answer that question and figure out which question you're really being asked are you asked about the magnetic field lines around a magnet or within the magnet so be careful with that so let's next take a look at the interaction between two of these lovely bar magnets I've got two identical ones here and so turns out that just with uh like we saw with electric charges like charges repel and Opposites Attract the same is going to be true of magnets and their corresponding poles so if I try to line up north pole with North Pole there's a repulsion here they do not want to stick whatsoever same thing with South Pole and South Pole but if I take and line up north to south they stick and it works either way if I flip them both over and still line up south to North they're still going to stick and now there's an attraction instead of a repulsion same thing if I try to line them up lengthwise instead of end to end again if I line up South to South north to North they repel each other they don't want to stick at all so but if I flip it around all of a sudden now and they stick yet again uh as well now why do we call them North and South well it turns out if you take a a ferromagnetic material like this one again so let's say I tie a string around the metal and just going to kind of rotate we'll find out that the north magnetic pole here always wants to point some whatat in the northern direction towards the North Pole of the earth well it turns out it's not exactly at the geographic North Pole of the earth it turns out is somewhere in the northern Hudson Bay or something like that uh but we'll get there in a minute so and if instead of tying a string here maybe you just want to take a piece of Styrofoam and float it in water and set this right on the styrofoam well the styrofoam will rotate until again the North End the North Pole end of the magnet points towards the North Pole if you will Points North well again if you recall how this line up with our other magnet so it wants to line up with the other magnet north to south south to North well it turns out it's interacting with the uh Earth's magnetic field when it kind of swivels around so that the North Pole points to the North and the Earth's magnetic field it's if as if the Earth has a big fat bar magnet in its core running across the Earth in a a north to south fashion approximately if you will well if the North End of of this magnet is pointing towards the North Pole well then the Earth's bar magnet must have a South Pole up at the north end this is getting confusing so it turns out what we call the geographic North Pole is actually the magnetic South Pole and what we call the geographic South Pole down in Antarctica is actually a magnetic north pole so it's kind of backwards and so some people might have properly called this the north seeking pole of a magnet and this is the South seeking pole of the magnet or something like this but uh it turns out their their name for historical reasons and we're stuck with with them now at this point uh and once again it also turns out that the geographic North Pole is not the same as the magnetic South Pole the magnetic South Pole is not all the way at the North Pole of the earth it's actually again in the northern Hudson Bay so and the geographic South Pole is not the same as the Magnetic North Pole the Magnetic North Pole turns out is off the coast of Antarctica somewhere not kind of in the center of Antarctica so and it turns out uh those are moving around a little bit as well and it turns out we don't know exactly why the Earth has a magnetic field now you might be like well maybe there's a big iron bar magnet in in the core of the earth so and the problem with that is that we believe the you know we have good evidence that the the core of the earth is actually molten melted liquid uh and iron fair amount of iron in there but not solid and and that's a problem so the reason this lovely substance right here is magnetized is that all the little localized regions in this lovely bar magnet are pointing a certain direction if you will their magnetic moments are aligned to point a certain direction so and by by doing that you know and you know Iron's a good pherom magnetic material so but not all Iron has been magnetized but if you put it in the proximity of a magnet for a long period of time it might get magnetized or if you scrape a magnet so over and over and over again against a piece of iron it might become magnetized and the idea is that you're aligning the different uh localized magnetic moments in such a way and it turns out at elevated temperatures you get more mobility of the localized regions and so it's easier to magnetize you know a pherom magnetic substance and stuff like that so but it's still in the solid phase is the key though and so they can permanently freeze with their magnetic moments more aligned in a certain direction well the problem if if the earth's core is liquid there's no way to permanently freeze those magnetic moments in a certain direction so well it turns out we're going to find out that uh electric currents result in magnetic fields and we kind of suspect that maybe then there's an electric current running through the Earth's core in some way shape or form and what the nature of that current is and what causes it and stuff we don't actually know uh but we do know that it's it's not fixed either so it is changing over time and and as a result both the location of the uh the Magnetic North Pole and the Magnetic South Pole those are changing a little bit over time as well and there's evidence to show that they actually will reverse in polarity uh every so many million years or something like this as well so let's go back and again do a quick review of electric fields and then we'll compare magnetic fields to those so I just want to go back and review real quick uh the direction of the the force of a particle in an electric field if you recall what must a particle have to feel a force in electric field well it must be charged so and the magnitude of the force is going to equal Q * the magnitude of the electric field and so if I have this positive charge right here in this electric field what would be the direction of the force that it's going to feel well for a positive charge it's in the same direction as the electric field so what if I swap that positive charge out and now make it a negative charge instead well for negative charge the force is in the opposite direction it's always in the opposite direction as the electric field so in this case the force would be pointing down so for a positive charge the force is in the same direction as the electric field for negative charg in the opposite direction cool so but the only thing a particle must have in order to fill this force is charge well let's swap some things out here so one let's go back and start with a positive charge again so but let's make this instead of an electric field now let's make it a magnetic field so it turns out the symbol for magnetic field is B so it will be measured in Tesla as the SI unit we'll find out that gaus is pretty common as well because a Tesla is pretty big there's 10 4th gaus equal to one Tesla but the Tesla is the SI unit all right so it turns out the equation relating the force to the magnetic field for a particle is a little more complex and there's a little more to it than this which we'll add in a little bit here but it's qvb and this is going to give us some intuition here that it means that for a particle to feel this force in a magnetic field it must be charged and it must have a velocity it must be moving so if I've got this positive charge just sitting here in this magnetic field well if it's just sitting there that means the velocity is zero which means the force is zero and it will not feel a force at all so we talk about the the force on a charge in motion for magnetism here it has to be in motion if the if the charge here is not moving it will not feel a magnetic force that was not true for an electric force it is going to be true for the magnetic force and again this is not intuitive it's just something we have discovered all right now it turns out there's a little more to this as well it turns out there's a little factor of sin Theta on here as well where Theta is going to be the angle between the velocity Vector so and the magnetic field vector so and it turns out well if you recall the S of 0 is zero and the sign of 180 is zero so and the sign of 90 is one so keep that in mind for just a second so if I start you know drawing in a velocity Vector here and let's say I say that this charge right here is moving straight up perfectly parallel with the magnetic field well that mean the angle between the velocity and the magnetic field would be Z and the sign of zero is also zero and so it turns out if your velocity and magnetic field are parallel there is no magnetic force there either so it's not just enough that it's moving it turns out that some component of the Velocity must be perpendicular to the magnetic field even just the slightest component well if it's parallel with it there is no component of the Velocity that's perpendicular to the magnetic field same thing if we switch that around and make that velocity point exactly the opposite direction here and now it's anti-parallel with the magnetic field but again that's also a condition where there is no no component that is perpendicular to the magnetic field and once again the magnetic force would be zero and again the sign of 180° with it being anti-parallel is also zero all right it turns out that the sign function reaches a maximum at 90° and the magnetic force therefore also reaches a maximum at 90° as well now notice there are some options for 90° here I could put it to the right I could put it to the left but we don't live in just a two-dimensional world we live in a threedimensional world and so it turns out anywhere in this horizontal plane that I direct it whether it's out of the board into the board left right or anything in between as long as it's in this horizontal plane we'll end up being perpendicular to the magnetic field and we'll reach a maximum of the force and here's where things are going to get just a little bit crazy so it turns out this is the result of what we call a cross product and for an algebra based course you definitely don't have to know what a cross product is it's usually something you encounter a little a little bit with Matrix algebra and maybe you get it in a college algebra class but you might get it in a straight up Matrix algebra course as well so but that's where this ultimately comes from and it turns out with a cross product figuring out the direction of a cross product well it turns out it's going to be orthogonal to both uh components of the cross product what that ultimately means in this case the components of the cross product are the velocity and the magnetic field and and our our force in this case is going to be perpendicular to both of those right now they form a plane the velocity and the magnetic field form a plane and that plane is the plane of the board to be perpendicular to that plane of the board you either have to be coming straight out of the board or going straight into the board and it turns out your force is always going to be mutually perpendicular to both the velocity and the magnetic field all right now which one is it how do we figure that out well it turns out we come up with what we call the right- hand rules for figuring this out and keep in mind they are right hand rules be careful about accidentally pulling out your left hand and things of swort as we'll see uh but they are the right-hand rules and we use them as kind of just ways of figuring out the direction of the force based on the given directions here and so the way this is going to work there's unfortunately multiple ways of presenting these right-hand rules and my apology for that it's just the way that it is uh I'm going to present one I might allude to some others that maybe it's presented for you if you've got a way that you've already learned it and stuff like that and you've got it you know kind of uh foundationally in your head already run with it don't use mine so but if you uh you haven't got one in your head you want a good Set uh mine's as good as any out there so all right way this is going to work you're going to line up your fingers with the magnetic field you're going to line up your thumb with the velocity and then the force is going to come out of your palm so let's see how this works here with this particular example right here so in this case you want to point your finger in the direction of the magnetic field so they're pointing straight up so where the magnetic field points but then you want your thumb to point in the direction of the Velocity so I had to flip it around pointing to the right and in this case then the force is going to come out your palm which in this case means it's coming straight out of the board now this is not the only way people do this some people do this instead of doing a straight open hand like this they'll kind of make it like a gun and they'll say finger in the direction so index finger in the direction of the magnetic field so thumb still in the direction of the velocity and then your middle finger is going to point perpendicular to both of these and point straight out well that's the same thing as your palm so uh either way uh those are functionally equivalent now some people will do this a little bit different they'll say well if it's really a cross product of v crossb and if it's V cross B you need to start off first with your fingers pointing towards V and then curl them up to B and then whichever way your thumb points that's the direction of the force so and that works too it's consistent it's reliable and tricky to in a matrix algebra class that's often how cross products are taught so however that is not the convention I'm going to be using so I will not allude to that from here on out so turns out we're going to learn like four different right-hand rules for different scenarios and magnetism here in this chapter and I'm going to be as consistent as I can with possible where uh my fingers are going to point in the direction of the magnetic field so and I'm going to have a velocity of some sort as we'll see with my thumb uh and we'll go from there all right so what if this had been a negative charge in instead so well with a negative charge just like an electric field the force felt by a positive charge in electric field is in the opposite direction as a force felt by a negative charge and the same is true for the magnetic force as well and so in this case if you point again your fingers in the direction of the magnetic field your thumb in the direction of the Velocity well for a positive charge the force comes out the Palm which means for a negative charge it goes the opposite direction out the back of your hand and into the board instead all right now it turns out that you can also decide to use a leftand rule for this one as well and if you use your left hand for a negative charge well then the force would still come out your palm and you have your fingers up your velocity to the right and then the force would still be coming out the Palm because you're using a left hand instead it gives you the opposite result I hate that just with a passion I had a student one time who just almost you know just instinctively always pulled out his left-handed to do the right- hand rule and so I hate get giving students an option of ever using a left- hand rule and so I like just saying hey do the right hand rule if it's a positive charge it comes out your palm if it's a negative charge it's just the exact opposite direction 180° so now we're going to take a look at three different applications of the right hand rule and uh in the first one we got a positive charge it's going to be moving to the left and it's going to enter a magnetic field that's directed upward and the question is what is the direction of the force so in this case we're going to line up our fingers in the direction of the magnetic field notice we got a lot of options which way we can rot that I'll have my fingers pointing up but we need our thumb to point to the left and for a positive charge again the force comes out the Palm which is into the board in this case so I'm going to write into the page because you're most likely going to see this you know into the screen or into the page of a book or something like that or into the board in this case so for the next one for a negative charge it would work exactly the same way and again make sure you're using right hand so fingers in the direction of the magnetic field Thumb in the direction of the Velocity but instead of coming out the Palm for a negative charge is the opposite direction coming out the back of the hand which would now be out of the page okay so similar to the ones we saw now uh we live in a three-dimensional world and all of these are inherently three-dimensional problems and so what if your magnetic field or your velocity uh instead of being up down left or right is either coming out of the page itself or into the page we need a way to represent that and it turns out that for something out of the page it's represented by a DOT or by a DOT with a circle around it same diff those mean directly out of the page coming out toward you so and it turns out going into the page is represented by an X like it's the uh tail of an arrow going into the board so to speak and it's either an X or it's an X once again with a circle around it either of those would mean something is being directed straight into the board all right so in this next example here we've got a positive charge with a velocity that's pointing up encountering a magnetic field that is directed out of the board and so if we apply our right hand rule so first thing I'm going have to get my fingers pointing out this direction in some way shape or form out of the board so and then I need my thumb to point up and so my hand is going to be oriented in just such a fashion with the magnetic force coming out the Palm for a positive charge and directed off to the right in this case case so you can see why this is sometimes rather humorous when you see students taking the test on this particular material and all over the room you could look around and students are kind of like you know tweaked and contorted into various positions and stuff like this trying to do these right- hand rules and it a little bit of pain in the butt but you really want to make sure you've got this down pat and get a lot of practice so with the directions on the right hand rules but also with calculations which is what we'll do next so this diagram is included with the question will be solving here it's right on the stud guide part of the question definitely needs to be given and the question says when the 1.0 micrum positive charge in the diagram enters the region with the 2.0 Tesla magnetic field directed into the page with a velocity of 1200 m/s directed to the right what is the magnitude of the magnetic force acting on it and what is the initial direction of the magnetic force all right so in this case with the magnetic field being directed into the page or into the board in this case and the velocity pointing to the right they are 90° apart and the sign of 90 is one and so uh the force here is going to be at a maximum so we've got f equals Q that's not a v v b sin Theta and in this case s of 90 is one so that term is going to kind of fall off here and so fals q and that 1 micr is going to be 1.0 * 10 -6 k velocity 1200 m/s so and then finally the magnetic field 2.0 Tesla that's a rather strong magnetic field the Earth's magnetic field is like 0.5 gaus and if you recall there are 10,000 gaus in one Tesla uh so two Teslas is pretty significant significantly stronger like 20,000 times stronger than the Earth's magnetic field all right but plug and chug from here and we can do this probably in our head here so uh 1 1200 * 2 2 is 2400 which is 2.4 * 10 3r and then * 1 * 10 6 would be 2.4 * 10-3 and this is going to come out in Newtons if we use SI units all the way across then SI unit for force will just kind of fall right out we could also write this as 024 Newtons as well so that's the first part of the calculation is what is the magnitude of the force and the second part of the question is what is the initial direction of the force in this case that's where the right hand rule is going to come into play and we want to point our fingers in the direction of the magnetic field that means into the board and we want to point our Thumb in the direction of the Velocity which means I'm going to have to orient it in such fashion like so and coming out my palm for a positive charge would be a magnetic force that is going to be directed upward so at least it is initially so keep in mind so once we get this positive charge in here it's going to have an upward force acting on it and that's going to change its trajectory and this thing's going to start veering off upward but as it veers off upward that's going to change our right hand rule as well if the dire if the uh direction of the velocity changes then your application of the right hand rule is going to change as well and so once again the magnetic field isn't changing so but instead of my thumb pointing to the right as this thing starts to change its trajectory my thumb's going to move up there as well and the force is going to change direction as well coming out my palm and it's going to change Direction all the time and what we'll find out is if this magnet this region of the magnetic field is big enough you'll probably get to a point or you potentially could get to a point where it just starts doing circles in the magnetic field and the whole time as it changes there's going to be a force directed towards the center of that Circle at all points so with uniform circular motion the force responsible for keeping it on that circular path you might recall is the Cent tripal Force so we got a couple of different ways uh this might be taken a step further so we calculated the magnitude of the force you might get a question that says well if you calculate the magnitude of Force if I give you the mass then what's the acceleration and you would just use Newton Second Law and say f equals Ma and plug in the mass and kilograms and use the force we just calculated and then you could solve for the acceleration the other way it could go is it might go and uh once again give you the mass of the particle and stuff like that it might say what's the radius of the circular motion after it enters the region with the magnetic field well in that case you'd want to say well okay some of the forces instead of equaling ma when there circular motion it equals the centripetal force of mv^2 over r as you might recall and so in this first example we'd be setting qvb sin Theta equal to Ma so in the second case we'd be setting qvb sin Theta equal to mv^2 over R so and again provided we were given the mass so we were already provided with the magnitude of the Velocity we could solve for the radius of that circular motion as well so just a couple of uh examples of how this could be taken a step further in a calculation if you found this lesson helpful consider giving it a like happy study

an introduction to magnetic fields and forces going to be the topic of this lesson in my new General Physics playlist which when complete will cover a full year of University algebra based physics now in this lesson we&#39;re going to start by taking a look at a simple bar magnet we&#39;ll use that to introduce magnetic field to kind of Trace them and we&#39;ll see some similarities to the electric dipole we saw in the last chapter and then we&#39;re going to take a look at the magnetic force acting on a charge in Motion in the associated calculations my name is Chad and welcome to Chad&#39;s prep where my goal is to take the stress out of learning science now if you&#39;re new to the channel we&#39;ve got comprehensive playlists for General chemistry organic chemistry General Physics and high school chemistry and on Chads prep.com you&#39;ll find premium Master courses for the same that include study guides and a ton of practice you&#39;ll also find comprehensive prep courses for the DAT the MCAT and the oat so we&#39;re going to start this lesson off by taking a look at the magnetic field lines around a simple bar magnet like this one and every bar magnet is what we call a magnetic dipole it has two poles every time you&#39;ve got a Magnetic North Pole and a magnetic South Pole those are the labels we give to them they&#39;re kind of opposite poles if you will uh and it turns out even if I cut this magnet in half and create two smaller pieces each of those pieces will also have a magnetic north and a magnetic South and if I cut those pieces in half each of the new pieces will have a magnetic north and a magnetic South and you can keep going on so it turns out that every bar magnet is going to have a magnetic north and a magnetic South Pole every time now in drawing the magnetic field lines it&#39;s uh instructive to go back and remind ourselves of what the electric field lines look like with an electric dipole Now with an electric dipole it&#39;s a little bit different because we actually we actually have separate point charges where with our bar magnet here it&#39;s one piece of metal or fom magnetic materials the case may be that has a north and a South Pole built into that single piece of metal but you might remind yourself an AIA question all electric field lines originate where and terminate where where well they all originate either on a positive charge or from infinity and terminate either on a negative charge or at Infinity so in this case with the electric dipole the electric field lines always go from positive to negative and we&#39;re going to find that the magnetic field lines around a bar magnet look very similar and they always go from north to south sort of as we&#39;ll see so it&#39;s going to look very similar here though but we&#39;re going to start with North and work our way around to South same thing around the other side here and we can make bigger field lines just like we did with the electric dipole as well and now we&#39;re going to see the one exception though is that there&#39;s actually uh electric I&#39;m sorry there&#39;s actually magnetic field lines going right through the bar magnet as well but from south to North so here&#39;s where we got to be careful if we said you know where do the electric field lines run in an electric dipole well always from positive negative period no exceptions but if we said where do the magnetic field lines run around a bar magnet so as long as we&#39;re talking around the bar magnet outside of the magnet it&#39;s from north to south but if we talk about through the magnet itself it&#39;s from south to North and so we got to be careful one how we ask that question but two how you answer that question and figure out which question you&#39;re really being asked are you asked about the magnetic field lines around a magnet or within the magnet so be careful with that so let&#39;s next take a look at the interaction between two of these lovely bar magnets I&#39;ve got two identical ones here and so turns out that just with uh like we saw with electric charges like charges repel and Opposites Attract the same is going to be true of magnets and their corresponding poles so if I try to line up north pole with North Pole there&#39;s a repulsion here they do not want to stick whatsoever same thing with South Pole and South Pole but if I take and line up north to south they stick and it works either way if I flip them both over and still line up south to North they&#39;re still going to stick and now there&#39;s an attraction instead of a repulsion same thing if I try to line them up lengthwise instead of end to end again if I line up South to South north to North they repel each other they don&#39;t want to stick at all so but if I flip it around all of a sudden now and they stick yet again uh as well now why do we call them North and South well it turns out if you take a a ferromagnetic material like this one again so let&#39;s say I tie a string around the metal and just going to kind of rotate we&#39;ll find out that the north magnetic pole here always wants to point some whatat in the northern direction towards the North Pole of the earth well it turns out it&#39;s not exactly at the geographic North Pole of the earth it turns out is somewhere in the northern Hudson Bay or something like that uh but we&#39;ll get there in a minute so and if instead of tying a string here maybe you just want to take a piece of Styrofoam and float it in water and set this right on the styrofoam well the styrofoam will rotate until again the North End the North Pole end of the magnet points towards the North Pole if you will Points North well again if you recall how this line up with our other magnet so it wants to line up with the other magnet north to south south to North well it turns out it&#39;s interacting with the uh Earth&#39;s magnetic field when it kind of swivels around so that the North Pole points to the North and the Earth&#39;s magnetic field it&#39;s if as if the Earth has a big fat bar magnet in its core running across the Earth in a a north to south fashion approximately if you will well if the North End of of this magnet is pointing towards the North Pole well then the Earth&#39;s bar magnet must have a South Pole up at the north end this is getting confusing so it turns out what we call the geographic North Pole is actually the magnetic South Pole and what we call the geographic South Pole down in Antarctica is actually a magnetic north pole so it&#39;s kind of backwards and so some people might have properly called this the north seeking pole of a magnet and this is the South seeking pole of the magnet or something like this but uh it turns out their their name for historical reasons and we&#39;re stuck with with them now at this point uh and once again it also turns out that the geographic North Pole is not the same as the magnetic South Pole the magnetic South Pole is not all the way at the North Pole of the earth it&#39;s actually again in the northern Hudson Bay so and the geographic South Pole is not the same as the Magnetic North Pole the Magnetic North Pole turns out is off the coast of Antarctica somewhere not kind of in the center of Antarctica so and it turns out uh those are moving around a little bit as well and it turns out we don&#39;t know exactly why the Earth has a magnetic field now you might be like well maybe there&#39;s a big iron bar magnet in in the core of the earth so and the problem with that is that we believe the you know we have good evidence that the the core of the earth is actually molten melted liquid uh and iron fair amount of iron in there but not solid and and that&#39;s a problem so the reason this lovely substance right here is magnetized is that all the little localized regions in this lovely bar magnet are pointing a certain direction if you will their magnetic moments are aligned to point a certain direction so and by by doing that you know and you know Iron&#39;s a good pherom magnetic material so but not all Iron has been magnetized but if you put it in the proximity of a magnet for a long period of time it might get magnetized or if you scrape a magnet so over and over and over again against a piece of iron it might become magnetized and the idea is that you&#39;re aligning the different uh localized magnetic moments in such a way and it turns out at elevated temperatures you get more mobility of the localized regions and so it&#39;s easier to magnetize you know a pherom magnetic substance and stuff like that so but it&#39;s still in the solid phase is the key though and so they can permanently freeze with their magnetic moments more aligned in a certain direction well the problem if if the earth&#39;s core is liquid there&#39;s no way to permanently freeze those magnetic moments in a certain direction so well it turns out we&#39;re going to find out that uh electric currents result in magnetic fields and we kind of suspect that maybe then there&#39;s an electric current running through the Earth&#39;s core in some way shape or form and what the nature of that current is and what causes it and stuff we don&#39;t actually know uh but we do know that it&#39;s it&#39;s not fixed either so it is changing over time and and as a result both the location of the uh the Magnetic North Pole and the Magnetic South Pole those are changing a little bit over time as well and there&#39;s evidence to show that they actually will reverse in polarity uh every so many million years or something like this as well so let&#39;s go back and again do a quick review of electric fields and then we&#39;ll compare magnetic fields to those so I just want to go back and review real quick uh the direction of the the force of a particle in an electric field if you recall what must a particle have to feel a force in electric field well it must be charged so and the magnitude of the force is going to equal Q * the magnitude of the electric field and so if I have this positive charge right here in this electric field what would be the direction of the force that it&#39;s going to feel well for a positive charge it&#39;s in the same direction as the electric field so what if I swap that positive charge out and now make it a negative charge instead well for negative charge the force is in the opposite direction it&#39;s always in the opposite direction as the electric field so in this case the force would be pointing down so for a positive charge the force is in the same direction as the electric field for negative charg in the opposite direction cool so but the only thing a particle must have in order to fill this force is charge well let&#39;s swap some things out here so one let&#39;s go back and start with a positive charge again so but let&#39;s make this instead of an electric field now let&#39;s make it a magnetic field so it turns out the symbol for magnetic field is B so it will be measured in Tesla as the SI unit we&#39;ll find out that gaus is pretty common as well because a Tesla is pretty big there&#39;s 10 4th gaus equal to one Tesla but the Tesla is the SI unit all right so it turns out the equation relating the force to the magnetic field for a particle is a little more complex and there&#39;s a little more to it than this which we&#39;ll add in a little bit here but it&#39;s qvb and this is going to give us some intuition here that it means that for a particle to feel this force in a magnetic field it must be charged and it must have a velocity it must be moving so if I&#39;ve got this positive charge just sitting here in this magnetic field well if it&#39;s just sitting there that means the velocity is zero which means the force is zero and it will not feel a force at all so we talk about the the force on a charge in motion for magnetism here it has to be in motion if the if the charge here is not moving it will not feel a magnetic force that was not true for an electric force it is going to be true for the magnetic force and again this is not intuitive it&#39;s just something we have discovered all right now it turns out there&#39;s a little more to this as well it turns out there&#39;s a little factor of sin Theta on here as well where Theta is going to be the angle between the velocity Vector so and the magnetic field vector so and it turns out well if you recall the S of 0 is zero and the sign of 180 is zero so and the sign of 90 is one so keep that in mind for just a second so if I start you know drawing in a velocity Vector here and let&#39;s say I say that this charge right here is moving straight up perfectly parallel with the magnetic field well that mean the angle between the velocity and the magnetic field would be Z and the sign of zero is also zero and so it turns out if your velocity and magnetic field are parallel there is no magnetic force there either so it&#39;s not just enough that it&#39;s moving it turns out that some component of the Velocity must be perpendicular to the magnetic field even just the slightest component well if it&#39;s parallel with it there is no component of the Velocity that&#39;s perpendicular to the magnetic field same thing if we switch that around and make that velocity point exactly the opposite direction here and now it&#39;s anti-parallel with the magnetic field but again that&#39;s also a condition where there is no no component that is perpendicular to the magnetic field and once again the magnetic force would be zero and again the sign of 180° with it being anti-parallel is also zero all right it turns out that the sign function reaches a maximum at 90° and the magnetic force therefore also reaches a maximum at 90° as well now notice there are some options for 90° here I could put it to the right I could put it to the left but we don&#39;t live in just a two-dimensional world we live in a threedimensional world and so it turns out anywhere in this horizontal plane that I direct it whether it&#39;s out of the board into the board left right or anything in between as long as it&#39;s in this horizontal plane we&#39;ll end up being perpendicular to the magnetic field and we&#39;ll reach a maximum of the force and here&#39;s where things are going to get just a little bit crazy so it turns out this is the result of what we call a cross product and for an algebra based course you definitely don&#39;t have to know what a cross product is it&#39;s usually something you encounter a little a little bit with Matrix algebra and maybe you get it in a college algebra class but you might get it in a straight up Matrix algebra course as well so but that&#39;s where this ultimately comes from and it turns out with a cross product figuring out the direction of a cross product well it turns out it&#39;s going to be orthogonal to both uh components of the cross product what that ultimately means in this case the components of the cross product are the velocity and the magnetic field and and our our force in this case is going to be perpendicular to both of those right now they form a plane the velocity and the magnetic field form a plane and that plane is the plane of the board to be perpendicular to that plane of the board you either have to be coming straight out of the board or going straight into the board and it turns out your force is always going to be mutually perpendicular to both the velocity and the magnetic field all right now which one is it how do we figure that out well it turns out we come up with what we call the right- hand rules for figuring this out and keep in mind they are right hand rules be careful about accidentally pulling out your left hand and things of swort as we&#39;ll see uh but they are the right-hand rules and we use them as kind of just ways of figuring out the direction of the force based on the given directions here and so the way this is going to work there&#39;s unfortunately multiple ways of presenting these right-hand rules and my apology for that it&#39;s just the way that it is uh I&#39;m going to present one I might allude to some others that maybe it&#39;s presented for you if you&#39;ve got a way that you&#39;ve already learned it and stuff like that and you&#39;ve got it you know kind of uh foundationally in your head already run with it don&#39;t use mine so but if you uh you haven&#39;t got one in your head you want a good Set uh mine&#39;s as good as any out there so all right way this is going to work you&#39;re going to line up your fingers with the magnetic field you&#39;re going to line up your thumb with the velocity and then the force is going to come out of your palm so let&#39;s see how this works here with this particular example right here so in this case you want to point your finger in the direction of the magnetic field so they&#39;re pointing straight up so where the magnetic field points but then you want your thumb to point in the direction of the Velocity so I had to flip it around pointing to the right and in this case then the force is going to come out your palm which in this case means it&#39;s coming straight out of the board now this is not the only way people do this some people do this instead of doing a straight open hand like this they&#39;ll kind of make it like a gun and they&#39;ll say finger in the direction so index finger in the direction of the magnetic field so thumb still in the direction of the velocity and then your middle finger is going to point perpendicular to both of these and point straight out well that&#39;s the same thing as your palm so uh either way uh those are functionally equivalent now some people will do this a little bit different they&#39;ll say well if it&#39;s really a cross product of v crossb and if it&#39;s V cross B you need to start off first with your fingers pointing towards V and then curl them up to B and then whichever way your thumb points that&#39;s the direction of the force so and that works too it&#39;s consistent it&#39;s reliable and tricky to in a matrix algebra class that&#39;s often how cross products are taught so however that is not the convention I&#39;m going to be using so I will not allude to that from here on out so turns out we&#39;re going to learn like four different right-hand rules for different scenarios and magnetism here in this chapter and I&#39;m going to be as consistent as I can with possible where uh my fingers are going to point in the direction of the magnetic field so and I&#39;m going to have a velocity of some sort as we&#39;ll see with my thumb uh and we&#39;ll go from there all right so what if this had been a negative charge in instead so well with a negative charge just like an electric field the force felt by a positive charge in electric field is in the opposite direction as a force felt by a negative charge and the same is true for the magnetic force as well and so in this case if you point again your fingers in the direction of the magnetic field your thumb in the direction of the Velocity well for a positive charge the force comes out the Palm which means for a negative charge it goes the opposite direction out the back of your hand and into the board instead all right now it turns out that you can also decide to use a leftand rule for this one as well and if you use your left hand for a negative charge well then the force would still come out your palm and you have your fingers up your velocity to the right and then the force would still be coming out the Palm because you&#39;re using a left hand instead it gives you the opposite result I hate that just with a passion I had a student one time who just almost you know just instinctively always pulled out his left-handed to do the right- hand rule and so I hate get giving students an option of ever using a left- hand rule and so I like just saying hey do the right hand rule if it&#39;s a positive charge it comes out your palm if it&#39;s a negative charge it&#39;s just the exact opposite direction 180° so now we&#39;re going to take a look at three different applications of the right hand rule and uh in the first one we got a positive charge it&#39;s going to be moving to the left and it&#39;s going to enter a magnetic field that&#39;s directed upward and the question is what is the direction of the force so in this case we&#39;re going to line up our fingers in the direction of the magnetic field notice we got a lot of options which way we can rot that I&#39;ll have my fingers pointing up but we need our thumb to point to the left and for a positive charge again the force comes out the Palm which is into the board in this case so I&#39;m going to write into the page because you&#39;re most likely going to see this you know into the screen or into the page of a book or something like that or into the board in this case so for the next one for a negative charge it would work exactly the same way and again make sure you&#39;re using right hand so fingers in the direction of the magnetic field Thumb in the direction of the Velocity but instead of coming out the Palm for a negative charge is the opposite direction coming out the back of the hand which would now be out of the page okay so similar to the ones we saw now uh we live in a three-dimensional world and all of these are inherently three-dimensional problems and so what if your magnetic field or your velocity uh instead of being up down left or right is either coming out of the page itself or into the page we need a way to represent that and it turns out that for something out of the page it&#39;s represented by a DOT or by a DOT with a circle around it same diff those mean directly out of the page coming out toward you so and it turns out going into the page is represented by an X like it&#39;s the uh tail of an arrow going into the board so to speak and it&#39;s either an X or it&#39;s an X once again with a circle around it either of those would mean something is being directed straight into the board all right so in this next example here we&#39;ve got a positive charge with a velocity that&#39;s pointing up encountering a magnetic field that is directed out of the board and so if we apply our right hand rule so first thing I&#39;m going have to get my fingers pointing out this direction in some way shape or form out of the board so and then I need my thumb to point up and so my hand is going to be oriented in just such a fashion with the magnetic force coming out the Palm for a positive charge and directed off to the right in this case case so you can see why this is sometimes rather humorous when you see students taking the test on this particular material and all over the room you could look around and students are kind of like you know tweaked and contorted into various positions and stuff like this trying to do these right- hand rules and it a little bit of pain in the butt but you really want to make sure you&#39;ve got this down pat and get a lot of practice so with the directions on the right hand rules but also with calculations which is what we&#39;ll do next so this diagram is included with the question will be solving here it&#39;s right on the stud guide part of the question definitely needs to be given and the question says when the 1.0 micrum positive charge in the diagram enters the region with the 2.0 Tesla magnetic field directed into the page with a velocity of 1200 m/s directed to the right what is the magnitude of the magnetic force acting on it and what is the initial direction of the magnetic force all right so in this case with the magnetic field being directed into the page or into the board in this case and the velocity pointing to the right they are 90° apart and the sign of 90 is one and so uh the force here is going to be at a maximum so we&#39;ve got f equals Q that&#39;s not a v v b sin Theta and in this case s of 90 is one so that term is going to kind of fall off here and so fals q and that 1 micr is going to be 1.0 * 10 -6 k velocity 1200 m/s so and then finally the magnetic field 2.0 Tesla that&#39;s a rather strong magnetic field the Earth&#39;s magnetic field is like 0.5 gaus and if you recall there are 10,000 gaus in one Tesla uh so two Teslas is pretty significant significantly stronger like 20,000 times stronger than the Earth&#39;s magnetic field all right but plug and chug from here and we can do this probably in our head here so uh 1 1200 * 2 2 is 2400 which is 2.4 * 10 3r and then * 1 * 10 6 would be 2.4 * 10-3 and this is going to come out in Newtons if we use SI units all the way across then SI unit for force will just kind of fall right out we could also write this as 024 Newtons as well so that&#39;s the first part of the calculation is what is the magnitude of the force and the second part of the question is what is the initial direction of the force in this case that&#39;s where the right hand rule is going to come into play and we want to point our fingers in the direction of the magnetic field that means into the board and we want to point our Thumb in the direction of the Velocity which means I&#39;m going to have to orient it in such fashion like so and coming out my palm for a positive charge would be a magnetic force that is going to be directed upward so at least it is initially so keep in mind so once we get this positive charge in here it&#39;s going to have an upward force acting on it and that&#39;s going to change its trajectory and this thing&#39;s going to start veering off upward but as it veers off upward that&#39;s going to change our right hand rule as well if the dire if the uh direction of the velocity changes then your application of the right hand rule is going to change as well and so once again the magnetic field isn&#39;t changing so but instead of my thumb pointing to the right as this thing starts to change its trajectory my thumb&#39;s going to move up there as well and the force is going to change direction as well coming out my palm and it&#39;s going to change Direction all the time and what we&#39;ll find out is if this magnet this region of the magnetic field is big enough you&#39;ll probably get to a point or you potentially could get to a point where it just starts doing circles in the magnetic field and the whole time as it changes there&#39;s going to be a force directed towards the center of that Circle at all points so with uniform circular motion the force responsible for keeping it on that circular path you might recall is the Cent tripal Force so we got a couple of different ways uh this might be taken a step further so we calculated the magnitude of the force you might get a question that says well if you calculate the magnitude of Force if I give you the mass then what&#39;s the acceleration and you would just use Newton Second Law and say f equals Ma and plug in the mass and kilograms and use the force we just calculated and then you could solve for the acceleration the other way it could go is it might go and uh once again give you the mass of the particle and stuff like that it might say what&#39;s the radius of the circular motion after it enters the region with the magnetic field well in that case you&#39;d want to say well okay some of the forces instead of equaling ma when there circular motion it equals the centripetal force of mv^2 over r as you might recall and so in this first example we&#39;d be setting qvb sin Theta equal to Ma so in the second case we&#39;d be setting qvb sin Theta equal to mv^2 over R so and again provided we were given the mass so we were already provided with the magnitude of the Velocity we could solve for the radius of that circular motion as well so just a couple of uh examples of how this could be taken a step further in a calculation if you found this lesson helpful consider giving it a like happy study

Transcript for:19.1 Introduction to Magnetic Fields and Magnetic Forces

Transcript for:
19.1 Introduction to Magnetic Fields and Magnetic Forces