hi it's mr. Andersen and this is ap physics essentials video 31 it's on the magnetic force imagine we have a charged particle like a proton moving through space since there's no force acting on it no field acting on it it's just going to keep going in that direction but if we have a charged particle that's moving by a magnetic field like it's rushing from the Sun and it's coming by the earth and the earth acts as a big magnet what it's going to do is it's going to apply a force to that and it's going to spiral into the planet and it causes the Northern Lights as these protons and electrons hit in our atmosphere we're giving off ionization colors and so as we move into magnetic forces we really are moving into a third dimension and so we have to have a way to deal with that so if we have just two dimensions it's easy to do that on a piece of paper but how do you do it with three dimensions a magnetic field for example coming at you or going away from you the way I remember it is it's like an arrow if an arrow is going through a hole you're just going to see that point on the end and so if you see concentric circles like that or a bunch of them that means the magnetic field is coming towards you and then the tail end of the arrow is going to look like that and so if we see a plus sign or X inside the circle that means that it's going away from us and that'll make sense when you see diagrams like this so we've got a magnetic field you can see that's coming out at us and let's say we have a charged particle that has no velocity it's just sitting there is there a magnetic force acting on that charged particle the answer is no if it's not moving there's no magnetic force but as it moves it has a velocity vector and if you're ever moving as a charged particle through a magnetic field then you're going to have a force applied to you and we call that the magnetic force or F sub n now things that you need to remember is that it's a perpendicular line between the magnetic force and the velocity and it's also perpendicular between the magnetic force and the magnetic field but the velocity vector in the magnetic field vector don't have to be perpendicular to each other how do we calculate the magnetic force well there are only three things that really deal with that first one is going to be Q that's going to be the charge of that particle in this case it would just be the elementary charge we then have the velocity vector or the speed of the particle and then we're going to cross product that with the magnetic field and what's a cross product well these two vectors when we when we multiply those together we're going to get a third vector that's going to move in a different dimension I got an animation that's going to show you that now depending on that angle we can get different amounts of this magnetic force and so we use sine theta to figure out how much that's going to vary over time and so let's say we have a magnetic field like this you can see that it is coming at us to figure out where that magnetic force is acting you have to use the right hand rule and so it takes a second to get this figured out but I'm going to hold my fingers out like this so I've got my index finger pointed out that's going to be the vector of the velocity so in other words where that charged particle is moving I then have my middle finger moving at 90 degrees to that and that's going to be the magnetic field and then the force is going to be your thumb and so you try to make these three dimensions with your finger and you can solve really intense problems like this you might look like an idiot as you're doing that but it's it's worth it so let's say we have a charged particle that has no velocity and it's in this magnetic field how big is our force going to be well we're not going to have a force again if it's not moving there's no force and so let me give you a harder problem let's say we have a magnetic field like this and we have a charged particle a positive particle that's moving up into the left and so how do you figure out where that magnetic force is going to be well first of all make your hand like this and then you're going to point your index finger in the direction of that moving charge so I'm moving it up and to the left then you want to make sure that your middle finger that magnetic field is pointed towards you because you can see on this diagram that the field is coming towards us and so once I've got that in order my thumb is going to show me the magnetic force and so that's going to go up and to the right so that was pretty easy to solve let's go to another one now we've got a different magnetic field and let's say that that charged particle that proton is moving from right to left how do you solve this one again stick your finger towards the left that's the movement of the particle now the magnetic field is not coming towards you it's going away from you so I have to turn my hand like this and now where's the magnetic force well you can see that that's going to be acting down what if we have one like this so we've got a different magnetic field what if we have an electron moving okay so if you have an electron moving there's two ways you can go at this number one you could just use your right hand and then just turn the force around when you're done or you've got a left hand and the left hand is going to work great so I'm going to put my finger point my index finger in the direction of the movement of the electron the magnetic field my middle finger in this case is going to come at me and so where's the force now the force is going to be to the left and so if you know the magnetic field and you know the direction you can always figure out where that magnetic force is going to be now the angle as I said is between the velocity and the magnetic field is not always 90 degrees and so we call that theta and depending on what that is we're going to get a different amount of that magnetic force and so those two are perpendicular but the third one is not going to be perpendicular and so here's our equation it's a little scary but it's not that bad q is going to be the charge V is going to be the velocity and then this is a cross-product between the two and so let's watch the animation before we get to the sine of theta and so if they're pointed in the same direction velocity and magnetic field we have no force but watch what happens when they become perpendicular we have a greater force or magnetic force if it moves to 180 degrees what's our magnetic force at this point it's going to be zero as I move it back to 90 degrees then it's going to be at its maximum at this time and so by using this sine theta in the middle we can figure out how much this cross-product or in other words multiplying the velocity times the magnetic field is affecting the overall magnetic force and so the parts of this formula are Q which is charged measured in coulombs V is going to be the vector velocity that's going to be in meters per second and then we have B which is going to be our magnetic field and we measure that in Tesla's and then as we solve for the magnetic force that's going to be measured in Newtons and so let's get to that theta in the sine of theta where's that coming from well let's say that our magnetic field and our velocity are perpendicular to each other we know that that's going to be the maximum amount of magnetic force that we can get what if it's this direction they're in opposite directions you remember what our our magnetic force is going to be here it's zero and if they're if they're both moving the same direction it's also going to be at zero and so if we just choose that angle to be theta and then we have sine of theta look what numbers we're going to get so if it's a zero degree angle sine of zero is going to be zero there's going to be no magnetic force likewise sine of 180 is going to be zero but if we're at ninety degrees that's going to be one and the AP folks say that you should really understand zero nine degrees 90 degrees and 180 but the sine makes sense to me and it should make sense to you as well what's our angle look like right here well that's around a 45 degree angle so what's the sine of 45 it's just going to be 0.7 zero it's going to be somewhere between one and zero and so if we do a problem like this calculate the magnetic force acting on a proton traveling at three point zero times ten to the fifth meters per second perpendicular to 0.32 Tesla magnetic field how could you figure out the magnetic force well you just start with your equation Q V sine theta of B what do I know well I know the magnetic field that's 0.32 Tesla's I know the velocity three point zero times ten to the fifth I know what the sine of theta is going to be because that's a 90-degree angle so that's going to be one the only thing I don't have it seems like is Q that's going to be the elementary charge so we just write that out like this and then we solve and we're going to have a really small force that's acting on that charged particle in that proton and so did you learn to apply mathematical routines to express the force exerted on a moving charge particle in a magnetic field always use your right hand and you'll probably need to calculate it to do the rest and I hope that was helpful
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