 Hi, I'm Zor. Welcome to a new Zor education. Today's lecture will be about Lorentz force. This is the force between the magnetic field and electric current. This lecture is part of the course called Physics for Teens, presented on unizor.com. I suggest you to watch this lecture from the website because every lecture including this one has very detailed explanation like a textbook basically And well all the lectures are obviously In the presented in the course so there is some kind of a logical Relationship between different lectures, so it's always good to go sequence in sequence lecture by lecture So you know exactly exactly What I'm talking during any lecture because you have listened to the previous one and I'm referring now on the same Website there is a math for teens course, which is very important for physics Especially vectors and calculus are used in physics everywhere Okay so Lorentz force Let me start with some repetition of What I have done in the previous lecture. We were talking about emperor model of Magnetic magnetic forces, so if you have let's say a straight line bar magnet north and south now the emperors model was related to little electrons which are Rotating around the nucleus now if all Atoms inside the magnet are aligned in such a way that electrons are Rotating around parallel axis Everywhere in this magnet and the planes of rotation obviously are parallel to each other and rotation is in exactly the same Direction then we have these magnetic qualities of the magnet If however atoms are chaotically Oriented so the axis are not parallel directions are different, etc. Then we don't have the magnetic properties So this is the result. Okay the magnetism results in Some kind of a synchronousness of the movement of the electrons inside the magnet now What emperor did next was let's just make a cross section of the magnet Well, and if we will view it from the top, we will see orbits of electrons These are all electrons lying in the same Plane plane of section right of cross section now look at this now all these electrons are Rotating in the same direction. So which means that this one And this one and this one they're all the same direction But what happens in this particular place in between the electrons? Well, one goes this way and other goes this way. So at any point inside the magnet Electrons are actually going against each other. It's the same direction But when they're touching each other, they are going into a different direction and they kind of neutralize There is no current one electron goes this way and I will go this way. I mean, they're still circulating in the same Direction if you will look from this, let's say it will be all counter wise counterclockwise or clockwise, but Wherever they touch each other There is no current one electron goes this way another goes Except at the edge So at the edge of the Cross-section there are only one directional all goes in the same direction this direction so This is the repetition. This is the emperors model of magnetism and as a consequence of this We have decided the following. Let's just take a wire Make a loop and Let's say there is some kind of electric current in it. So there is a source of electricity plus and minus and Considering this is the correct model and the model does basically represent very very well represent actually magnetic qualities This is supposed to possess the same magnetic qualities. I mean to have a loop of electricity and It should have these magnetic quality, which means there is some kind of a polarity north and south and it should behave like a magnet and Experiments show that it did so from now on we will forget about what's inside the magnet and we will talk about electric properties of the closed loop and With current running in it and we are saying that there are some magnetic properties Well, what does it mean that it has magnetic properties? Well, for example If you will take a let's say an arrow a compass it will orient itself along the magnetic lines of the earth because earth is a giant magnet Same thing with the loop of Electricity the wire loop where the electricity is running if we will allow it Let's say we put it on some kind of a floating device and put it in the water. So this particular Construction will orient itself along the magnetic lines of the earth. It will just turn like a compass basically and This is extremely important So from now on we will talk about these closed loops of wire and the magnet magnetic field and what happens if we will put this closed loop of Electric wire inside the magnetic field. Okay, here is the experiment. So let's say we have one magnet not sure I'm good a Represent representative of the pictures, but in any case I think I don't need this one this piece Let's say this is the only thing which I have and It goes like this Okay Does it look like a magnet? North and south so it's not a bar magnet. It's some kind of a horseshoe magnet. All right now What kind of magnetic field we have here well the magnetic field lines which we did talk about before are Going from north to south here and then inside the magnetic they go back Of course, they don't cross like on my picture. So this is the circulation of the magnetic field lines Okay, now let's take a Closed loop of wire in this case. I didn't really make a circle I made a rectangle It's kind of easier for me in this particular case and position is here in such a way that one Side of this rectangle will be close to one pole of the magnet and another to another so it's something like this Now let's assume that there is a electric current Which is going here. I will not I will not draw a source of electric current like here Plus and minus but we assume that there is some kind of a source here. All right, so there is an electric current which is running in this Rectangular wire loop. Okay Now what happens? Well, it has the magnetic qualities. It has poles now if I will look from this side and if direction is From plus to minus is this way then the North-south line will be perpendicular to this Loop, right? so if I'm Looking from this side if loop looks like this Then my north-south line would be perpendicular to the board if I'm looking From the top Then my loop looks like a line, right? Then magnetic poles would be North-south Right on this board. So the loop goes like my hand inside the The board and then the perpendicular to the plane of the Loop Line through its center would be the center would be the line between north and south pole So in this particular case my north-south line is perpendicular to the Board Now what happens? well, let's imagine that there is some kind of a axis of rotation so So I'm kind of mechanical device is here. So my loop can rotate around this axis So if initially my position is like this in the north-south line of This loop as a magnet is perpendicular to the board. We were talking about Alignment between the north-south line of Of this electric electric loop Aligning along the magnetic Lines of external field like a compass arrow of the compass aligning Along the magnetic lines of the earth in this case these are magnetic lines now if my North-south line of this Loop which has magnetic property is perpendicular. It will try to turn obviously along. So my wire loop will turn in such a way that It will take this position so the North-south line Would be here Along the lines of my external magnetic field. So it will turn Now which turn it's a different question, but we will talk about this, but it will turn now What happens when it will turn what happens with it with the? compass arrow Well, after it will turn towards The Norse it will bubble a little bit and will basically will be stable in this position pointing north, right? I mean north Edge of the arrow compass will point to the geographical north of the earth, which is actually south Pole of the earth as a magnet Okay So same thing here the north side north pole of this Loop as a magnet will point to the south pole of the external magnetic field Now if it's Fixed on this axis and this can turn now there is some some some kind of a force, right? Which which turns it? So what is this force? Well the force exists between magnetic field and the current So there is a current here, right? Now as long as there is a current and this current is in in this particular loop It will turn now. Let's think about how it works well, let's go back to initial position when I have this type of When one age is close to one and another age close to another pole and look at this from the top, all right So what do we see from the top from the top? We will see our wire loop as a line and I have two spots for the poles, okay So that's what you will do So this would be one pole This would be another pole and They're connected behind the board Now my wire initially would be like this line so It's basically like my head So you see only the top of this thing and north-south direction would be something like this now Why now and the axis of rotation would be perpendicularly to the board now Why does it Turn in such a way that the north will point to the south pole of the external back as well Obviously, there is some kind of a force I mean it doesn't do it by itself It should be the force which which actually moves it now. What happens as We are turning Let's say turns this way We still have a force the forces are actually acting on every Part of this rectangle now you just see it from the top But every side of this rectangle Experiences that this force what's next well next it will turn a little bit more still forces But you see now the forces are equalizing each other if before we had a Some kind of a torque because one force But in this position one force this and one force here and obviously they turn it around the axis but now when everything is aligned both forces are acting against each other and Basically, there is no more movement So whenever it will reach this position It will maybe wobble a little bit because of inertia and it will stabilize in this particular case That's what's happening. So what we have established that there is some kind of a force which acts between the magnetic field and the current So let's talk about this particular force and let's forget about our loop and let's talk about only one straight line with electric current running in it positioned in a magnetic field in the uniform magnetic field for simplicity because we are assuming that this Magnetic field is uniform. I mean for instance if you have a bar magnet North-south It's not really uniform. I mean this is much more complex story, but if you have a large Magnet like this with very long parallel lines Then you can assume basically Approximately that the field is uniform and that's what we are going to do right now. That's talking about electric current In the magnetic field and what kind of a force or Lord it's force basically acts on it Well the way how we will present it is the following so let's say we have the magnet again This is one pole and this is another pole I Will try to again do it in Three-dimension Let's say this is north. This is south So these magnetic lines are like this Now let's consider that our wire is like this This is the direction of the current Well, we were talking that electric Wire well if you have a loop then you have for instance in the rectangular form Then you have four different segments of the wire with current running in different direction So experiment shows that if you have a Wire with a current running in it in a magnetic field like this There is a force which acts actually on this particular wire and the only thing which we have to establish is the Direction of this force well again experiment shows the direction of the force can be determined by the rule of the right hand and That actually looks like this if If your magnetic field lines are entering your hand and your thumb points towards the Current then finger will point to the direction of the force This is the current and This is magnetic field Now in this case we have a very simple situation When electric current is perpendicular to the magnetic forces now What happened if this is a rectangular frame? Loop with the current Well, if you will look at this like this This is the final position, but in any case If this is the current this way, this is current this way Magnetic field goes this way. So if you will use this rule of the right hand then magnetic Force well Lorden's force actually which acts on this one and then this one would be perpendicular to both Okay, so again forces perpendicular to both lines of the magnetic field and the current line So if this is current And this is magnetic force then the perpendicular to both would be towards This direction and in this case towards this direction. So if this Loop is in this position both forces are neutralizing each other But if it's turned a little bit then there is a moment Which turns it around So in any case depending on and by the way, there is a current here as well, right? And there is also the force it's perpendicular to both in this case It goes up and this cases goes down and again in this final position all four forces are neutralizing each other So force acts on the current so let's forget about more complicated case of the wire loop and concentrate only on one particular Straight line which is in this case perpendicular to magnetic field now, let's just think about some kind of quantitative dependency between the force and Components which actually make this force well first of all obviously there is a current Now if there is no current there is no force if there is some current there is some force So it prompts us to think that It's probably proportional The force should be proportional to the current like if i is equal to zero f is equal to zero if i is if i is Equal to something then f is also some substantial value, right? Now let's think about what is i i is the current it's actually the number of electrons which are crossing certain lengths Per unit of time, right? That's what current actually is Number of coulons per per time coulons per seconds something like this, right? That's what one ampere is one coulon per second And per coulon is basically a quantity of electrons different different Unit size, but this is a number of electrons So what happens here? The higher the i the more magnetic lines Electrons are crossing per unit of time So it looks like it should be proportional and it is so f is Proportional to i now next If you have a short wire There is some kind of a force and then another Piece of wire there is another force if you have a twice as big piece of wire Then the forces are combined So the force must be Proportional to the lengths, right? And finally There is something which is a strength of the magnetic field which we don't really know what it is But definitely if you have a stronger magnet and again experiments show that this is true stronger magnet Pushes stronger, right? So there is also some kind of a characteristic Which we can call as strengths of the magnetic field or just magnetic field or intensity of the magnetic field probably intensity would be a better term so there is something which characterizes the intensity of the magnetic field and We can put the equal sign here in this particular case now Let's think about a little bit more if I will turn the wire so instead of This I will put it exactly parallel to magnetic lines Electrons in this case would not cross any magnetic lines and there will be no force So the force exists only if my electrons are crossing magnetic lines and Also experiment shows that it's actually perpendicular to the direction of the electrons and Direction of the magnetic lines like in this particular case when my field When my field is perpendicular to line the force is perpendicular to both of them Now what does it remind you that one vector is perpendicular to two other? it's actually a vector product and Obviously it should be proportional proportional to the angle between Direction of the Electric current and direction of the magnetic lines Because if there is parallel Phi is equal to zero between them so the angle Then the result is zero if they're perpendicular That's the largest force because the largest number of magnetic lines are crossed by electrons per unit of time and Then the sign is maximum for 90 degrees perpendicular and that would be just so if be is Absolute value of the magnetic strength and Phi is an angle between the direction of the current and direction of the magnetic lines Then this is the value of the force Obviously in certain units of measurement, right, but we don't have the units of measurement of the be right yet Good we will introduce these units of measurement exactly from this formula And we're saying that the unit is equal to 1 in this case. We call it Tesla Obviously to honor a guy by the name Tesla so one Tesla It's such a field that will give me One newton if it's one ampere times one meter one tesla And sign of 90 degree When it's perpendicular so this is a definition now Using this formula. We are defining the strengths of magnetic field in teslas So one tesla is such a field that if you have a one meter Wire positioned perpendicularly to this field And there is one ampere of electricity running In this wire Then the force will be one newton and that's the definition of the strengths of the magnetic field. So that's how we introduce the strengths of the magnetic field and the last Which actually follows very closely from this For those of you who remember What is the vector product? I can express this slightly differently because i and b are Vectors b is a vector directed from north to south and i is from plus to minus And if you have a vector product well l in this case is just a Scalar multiplier So if you will multiply As a vector product and what is the vector product? Well, it's vector which is perpendicular to both of them and its magnitude is equal to Magnitude of one magnitude of another and the sign of the Angled from one to another So this is basically the formula for loren's force I do suggest you to read the notes for this lecture. So you go to unisor.com Go to physics for teens electromagnetism and in In the section Which will be presented to you you will find the loren's force lecture Among other magnetism related Lectures Well, that's it for today. Thank you very much and good luck