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Aug
23
comment Showing that the magnetic field inside an infinite current carrying cylinder is zero
I know how to use Ampere's law to show this. I really wanted to follow the reasoning in the question. The point of the question is to figure it out without Ampere's Law. Also, your answer is not correct. My equation for B applies at all points except r = 0. According to your line of reasoning K in Coulomb's law would have to be zero or else the electric field of a single point particle would be infinite at r = 0. But that's wrong, because Coulomb's law is only valid for non-zero r.
Aug
23
accepted Showing that the magnetic field inside an infinite current carrying cylinder is zero
Aug
23
comment Showing that the magnetic field inside an infinite current carrying cylinder is zero
Let us continue this discussion in chat.
Aug
23
comment Showing that the magnetic field inside an infinite current carrying cylinder is zero
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
comment Showing that the magnetic field inside an infinite current carrying cylinder is zero
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
comment Showing that the magnetic field inside an infinite current carrying cylinder is zero
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
comment Showing that the magnetic field inside an infinite current carrying cylinder is zero
I shouldn't have to compute a line integral. The book hasn't covered it yet.
Aug
23
comment Showing that the magnetic field inside an infinite current carrying cylinder is zero
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
comment Showing that the magnetic field inside an infinite current carrying cylinder is zero
@DavidZ It's not a contradiction if a = 0, which is precisely what I'm trying to show.
Aug
23
comment Showing that the magnetic field inside an infinite current carrying cylinder is zero
Thanks, fixed. I showed generally, that the field form holds in empty space which would include outside or inside the cylinder as the charge is located on the cylinder's surface. This is a freshman physics question so it shouldn't be that hard. I just can't think of it, and it's bothering me.
Aug
23
revised Showing that the magnetic field inside an infinite current carrying cylinder is zero
edited body
Aug
23
revised Showing that the magnetic field inside an infinite current carrying cylinder is zero
edited body
Aug
23
asked Showing that the magnetic field inside an infinite current carrying cylinder is zero
Aug
14
awarded  Tumbleweed
Aug
10
revised Using the Mirror Rule to determine the magnetic field of an infinite slab
edited tags
Aug
10
accepted potential difference across a bulb
Aug
7
revised Using the Mirror Rule to determine the magnetic field of an infinite slab
added 431 characters in body; edited title
Aug
7
asked Using the Mirror Rule to determine the magnetic field of an infinite slab
Jul
18
accepted Applying Biot-Savart to a circular loop along central axis
Jul
18
comment Applying Biot-Savart to a circular loop along central axis
As for the symmetry argument, I'm visualizing B being perpendicular to the vector going from the circle to the point along the axis, as we keep changing this vector, we rotate it around in a circle, hence so does the vector B, but this is a circle in the y-z plane, hence B traces out a circle in the y-z plane and does not have a variable x component. Is that the kind of argument you were thinking of? I think it works! I come from math, and am not used to these kinds of non-rigorous arguments, but I'm growing quite fond of this kind of thinking.