28. Magnetic Fields and Forces

Force on Moving Charges & Right Hand Rule

# Anderson Video - Magnetic Force Right Hand Rule

Professor Anderson

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Let's talk about the magnetic force. What we learned yesterday is if a charge is moving and it's in a B field it feels a force. What force does it feel? It feels this. q v B sine theta. What is this stuff? This is obviously the force that it feels. q is the charge. v is the speed as measured by you. In the laboratory rest frame what speed v do you measure? B is the magnetic field. And theta is the angle between the velocity V and the B field, B. The magnetic field B. So force, we know, is a vector, this is the magnitude, how do we determine the direction? Well, let's write it down again. q v B sine of theta and then we put an n hat on there which is a direction that makes it a vector. And this direction, we have to use something called the right hand rule to determine the direction. q is the charge so it could be positive or negative. You always use the right hand rule to determine the direction, and then if it's a negative you flip that direction. v is a speed, B is a magnetic field, theta is the angle between those two. So we need to say a little bit about this. The right hand rule. Okay. And this is slightly tricky because of this learning glass approach, so I'll talk you through it and hopefully we can make some sense of it. So let's write this down again the magnetic force, we said, was q v B sine theta n hat. And now let's determine this n hat, what direction is it? Well, turns out that direction is given by your thumb if you take the velocity V and you put your fingers in the direction of V, and you take your fingers bent into the direction of B F v B Fingers- let's clarify this one a little bit, we're gonna say fingers straight for that first one and then fingers bent for B Alright so let's see if we can figure that out. I'm gonna draw your hand. There's your hand, okay, and we'll put a thumbnail on it so you know which way your hand is pointing. Nice pink shade, there we go. And this is your right hand. The force is the direction of your thumb. The fingers straight are the direction of the velocity v, the fingers bent are the direction of the B field lines And so here's how you do it. Okay let's say that we have the following system. We've got an x y z coordinate system, x y z and we're gonna have a particle that is moving along to the right. Velocity v, It is in a magnetic field B pointing up. and now we need to figure out the direction of the force on this particle. And so we can use the right hand rule to do that. So now I'm gonna demonstrate this to you but because we're flipping the image I've got to use my left hand and so don't look at me through the glass, look at the monitor over there and see if you can follow along Okay, so hold up your right hand. Okay? Everybody got the right hand up? The direction of v is to the right, so put your fingers straight in the direction of v. There we go. I'm gonna curl my fingers into the direction of B. B is going up, so curl your fingers until they're going up. Your thumb is now the direction of the force. And if you look at the monitor, it should look like that force is coming towards you Which in our coordinate system, would be coming towards you out in the x-direction. v cross B gets me a force that's coming out. And hopefully everybody is familiar with this vector sign, a circle with a dot is coming out of the screen towards you. So if you're looking at this at home on your computer, it's coming out of the screen towards you. And this is going into the screen. And this is like an arrow right? If you see a dot with a circle, that's the arrowhead coming right at you. If you see a circle with an x, that's the tails of the feather going away from you. So think of an arrow. Is it coming at me, do I see the tip? Or is it going away from me, do I see the feathers? Let's take- v we said was going up and B was going to the right. So v cross B should get me something that is going, I think maybe you're right, into the screen. Let's see. v going up, B to the right, that's this way which is away from you guys which is into the screen. I think I agree with you. Good. Let's try it for a different orientation. Let's say we do B going down, and V going to the right. Alright. v, fingers straight, B curl it. I still get something that's going into the screen Good. Let's try one more. B is going to the right, V is going down. Now how do I do that? Well I've got to put my fingers down for v, and then I curl them into the direction of B. So v cross B gets me something coming towards you guys, which is out of the screen. Good.

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