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Anderson Video - Magnetic Fields and Work

Professor Anderson
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About magnetic fields and work and let's say we do the following. Let's say we take a particle and we'll give it a positive charge. And now we're going to send it flying in this direction v. And let's put a magnetic field everywhere going into the page. As this particle flies through that magnetic field, it's going to feel a force. What direction is the force that it's going to feel? Is it up or is it down? Well, again we can use our right hand rule to determine that. So if you take your right hand and you put it in the direction of v with your fingers straight. And then you curl your fingers into the direction of B, it tells you that the force is going to be up. Okay, velocity to the right. Force going up. And in fact, that angle is a right angle. So let's go back to the definition of work for a second. Work is F d cosine of theta or F times v t cosine of theta, right? Distance is equal to velocity times time. And theta here is the angle between F and v. What's the angle between F and v in our case? It's a right angle. It's 90 degrees so I have cosine of 90 degrees. What's the cosine of 90 degrees? It's zero. And we just did this in general, right? This wasn't anything very specific. And so we can come up with a statement about magnetic fields and work which is the following. Magnetic fields do no work. They do no work on the particle. And that we can in fact take advantage of.