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Anderson Video - Motion of Charge in Fields

Professor Anderson
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So, let's say that we're going to think about an E field first. Okay, let's say I have the following picture. Here's my 3D coordinate system x y z. And let's draw our E field everywhere to the right. Okay, and let's say that we have a charge which is initially moving in the x direction. Here comes my charge, it's a positive charge, and it's going to move in the x direction. What is the electric field going to do to this charge? Well, we know that if it is a positive charge, plus q, it's going to feel a force due to that electric field and so eventually it's going to start moving in the positive y direction. It's going to bend around and eventually come in the positive y direction. It will eventually be parallel to E. But let's do the same thing now and think about the motion of q in a B field So let's draw the same thing, here's our coordinate system x y z. And now let's have this q initially moving in the x axis direction. Okay, well if my B field is now pointing everywhere to the right, then there has to be a force on this thing, right? And the force on it we determine from our right hand rule. So we've got a v coming out in the x direction, we've got a b going back to the right, so I've got to figure out how to rotate my hand such that I can do that properly, and if I do that just right, you guys can try it my arthritis is kicking in. That's how you know physics majors, right? Because they walk around the hall and they go like this all the time. What you should get is the following: v cross B is going to get me a force that's going up and so it's going to start bending up. And now when it's going up it's going to feel a force to the right, and then when it's going back it's going to feel a force down, and then eventually we'll come back around to where it started. Okay, and so you're going to get a v cross B force that makes it move in a circle, and that circle is always perpendicular to the B field. The force is perpendicular to the velocity and the B field and therefore this circle is perpendicular to the B field. In other words, the circle lies in the x z plane. That's what we're trying to draw here, we're trying to draw a circle in the x z plane