Timeline for Showing that the magnetic field inside an infinite current carrying cylinder is zero
Current License: CC BY-SA 3.0
13 events
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Aug 23, 2015 at 19:37 | vote | accept | user7348 | ||
Aug 23, 2015 at 5:31 | comment | added | user7348 | Let us continue this discussion in chat. | |
Aug 23, 2015 at 5:31 | comment | added | Timaeus | @user7348 I think maybe you were already assuming continuity if you were taking lots of partial derivative here there and everywhere inside. Partial derivatives don't exist if it isn't continuous on the direction you are taking the partial. | |
Aug 23, 2015 at 5:27 | history | edited | Timaeus | CC BY-SA 3.0 |
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Aug 23, 2015 at 5:25 | comment | added | user7348 | Given that's it's a very basic book, you think the author just wants me to assume continuity and take the limit, and be done with this problem? | |
Aug 23, 2015 at 5:16 | comment | added | Timaeus | @user7348 There are versions of electromagnetism where the value at any one point does matter only average values over regions of finite (nonzero) volume matter. But in those versions no information is given by saying the value at the origin is zero since the value at any one point doesn't matter. | |
Aug 23, 2015 at 5:10 | comment | added | user7348 | This is an introductory physics book and we have defined curl as a vector derivative, so it has 3 components that go like a cross product. | |
Aug 23, 2015 at 5:08 | comment | added | Timaeus | @user7348 The definition of a curl should be in terms of a line integral. There are other definitions are curls that only work if the field has partial derivatives in all directions, which then requires continuity. It might help if you say what you do know. | |
Aug 23, 2015 at 5:08 | comment | added | user7348 | If magnetic fields are continuous in empty space it's trivial. We require Lim(B) as r --> 0 = B(0) = 0 therefore a = 0. But, the author never mentioned magnetic fields are continuous in empty space, and I can't think how to prove this. | |
Aug 23, 2015 at 5:04 | comment | added | user7348 | I shouldn't have to compute a line integral. The book hasn't covered it yet. | |
Aug 23, 2015 at 4:58 | history | edited | Timaeus | CC BY-SA 3.0 |
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Aug 23, 2015 at 4:57 | comment | added | user7348 | I've been thinking along these lines for hours. To answer your question, B = $\frac{a}{r}$ of course. I've been thinking about taking the limit as r goes to 0, but there is absolutely no reason why lim(B) as r --> 0 must be 0. It's just not true that the limit of a magnetic field as it approaches a point has to equal the field at that point. For example, there is a discontinuity in the electric field of a sphere as you move from inside to outside. | |
Aug 23, 2015 at 4:42 | history | answered | Timaeus | CC BY-SA 3.0 |