Timeline for What is magnetic flux? How is it related to Faraday's law?
Current License: CC BY-SA 3.0
18 events
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| May 4, 2017 at 13:02 | history | edited | Mike | CC BY-SA 3.0 |
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| May 4, 2017 at 6:35 | comment | added | John | Let us continue this discussion in chat. | |
| May 3, 2017 at 14:41 | comment | added | Mike | Sure thing. These were all very good questions you asked here. It shows you're really thinking about these concepts. And don't get discouraged if you find this stuff confusing; all the best physicists have also been confused about it. | |
| May 3, 2017 at 14:34 | vote | accept | John | ||
| May 3, 2017 at 14:34 | comment | added | John | Sorry, I didn't read that comment. Thank you for the answer :) | |
| May 3, 2017 at 14:33 | comment | added | Mike | Yes, I think the potential difference should be zero around the rim. That's what I said three comments ago. Also, I've added a paragraph about differentiating the area. I think it should be helpful. | |
| May 3, 2017 at 14:31 | history | edited | Mike | CC BY-SA 3.0 |
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| May 3, 2017 at 14:24 | comment | added | John | Won't the potential difference between any two points on the rim of the disk be 0? | |
| May 3, 2017 at 13:21 | comment | added | Mike | The area of integration is not just a scalar number here; it is a geometrical surface that is changing in time. In the context of these equations, that surface is described at each point by the infinitesimal unit normal, $d\vec{A}$. If the surface is moving, that $d\vec{A}$ can change. In a very important sense, that's what's getting differentiated. I'll explain a little more in the answer. | |
| May 3, 2017 at 13:19 | comment | added | Mike | Regarding EMF around the disk, that's a good question, and there are several ways you could approach it. First, you could just place your two contacts at opposite edges. But then the simplest model for the circuit would have it going straight across the disk. You could also place the contacts close together along the edge, and then see how it varies as you slowly move the contacts farther apart. In each case, I predict no EMF because the velocity will be an odd function of distance along the line joining the contacts, so contacts at the same radius will lead to an integral of 0. | |
| May 3, 2017 at 12:32 | comment | added | John | And what exactly does differentiating the area of integration mean? Isn't the area of our surface a constant? Its position changes, but the area remains unchanged, right? | |
| May 3, 2017 at 12:12 | comment | added | John | I see... so if we wanted to measure the emf 'around' the disk, how would we connect the galvanometer? And will there be any eddy currents formed in this case? I can see that the rim of the disk will be at a potential difference from the center, but the current can only flow if there is a closed loop, which is only possible for the radii we've connected the galvanometer to. | |
| May 3, 2017 at 12:12 | history | edited | Mike | CC BY-SA 3.0 |
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| May 3, 2017 at 12:08 | comment | added | Mike | I've edited my answer to emphasize that the real physics content here is Jackson's point about choosing the surface with respect to the medium. So that explains why it has to move. As to why we choose a radius instead of a diameter or a chord: we certainly could choose a diameter or a chord, but then we'd be calculating the electromotive force around a loop that includes that diameter or chord. So when you're doing the experiment, you'd have put your galvanometer contacts at either end of that diameter or chord. You can certainly do that; it's just not the usual problem we talk about. | |
| May 3, 2017 at 12:05 | history | edited | Mike | CC BY-SA 3.0 |
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| May 3, 2017 at 12:04 | comment | added | John | I can't say I understood it all; for one, I'm unclear on what you mean by 'differentiating the area', but the biggest question I have is how do we choose the surface? Could we not have chosen a diameter, or a chord rather than a radii? Also, why does naively calling the flux the 'area swept' times the magnetic field in this case give the correct answer? | |
| May 3, 2017 at 11:58 | history | edited | Mike | CC BY-SA 3.0 |
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| May 3, 2017 at 11:53 | history | answered | Mike | CC BY-SA 3.0 |