Talk:Biot–Savart law

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I reestablished the version of 12 May 2012 because later versions where corrupted. It seems as if 151.135.188.206 was trying to edit the page, but he corrupted it. (Lejarrag, May 20, 2012) — Preceding unsigned comment added by Lejarrag (talk • contribs) 15:41, 20 May 2012 (UTC)

Nice, and thanks. Those IP's were fiddling around unecerssarily, and in cases blanking and obliterating. In addition I cleaned up the notation. F = q(E+v×B) ⇄ ∑_ic_i 17:12, 20 May 2012 (UTC)

edits all the way..

I have already just made some changes now. But...

• To my despair this article is written in the corny 2nd person "To apply the equation, you choose a point in space at which you want to compute the magnetic field. Holding that point fixed, you integrate over the path of the current(s) to find the total magnetic field at that point." It will be removed.
• Right now there is no indication that the integrals are line integrals in the equations. I'll modify that now.
• Also there is a contradictory notion of the "magnetic constant", initially it says μ₀ is the constant (permeability of free space), but later says $K_{m}=\mu _{0}/4\pi$ is the magnetic constant. I know I’m kicking up too much of a fuss for nothing, but is it actually a convention to use K_m in parallel with Coloumb's constant $k=1/4\pi \epsilon _{0}$? I've never seen it before... It will just be removed. If it is conventionally used then reinstate it (preferably with a referance so future pernickity editors like me will not go through this again).

Hope the edits are fine, and no one minds the fabulous colour boxes (Maschen - if you are reading this you will be proud of you're most succesful WP creation. I have used this all over the place, including this article). =) -- F = q(E + v × B) 00:30, 23 February 2012 (UTC)

• BTW why arn't the integrals line integrals $\int$ around a closed path $\oint$ ?? If the integral is around the path of electric current: how can current flow around a path not closed?
• And why is the constant $\mu _{0}/4\pi$ inside many of the integrals? I pulled it out from each - there is no reason to have it inside.
• I'll also merge the 1st two sections - too much overlap.

-- F = q(E + v × B) 01:11, 23 February 2012 (UTC)

somebody damaged the sidebar thing, ....

its not very nice now — Preceding unsigned comment added by 83.134.175.203 (talk) 23:13, 29 October 2012 (UTC)

It has been fixed :-) --Steve (talk) 00:24, 30 October 2012 (UTC)

Change of variable convention

I noticed that the variable for the point of application ($\mathbf {r}$), the parameter to $\mathbf {B}$, was written to be the same as the displacement vector from the line integral element $\mathbf {l}$ to that parameter $\mathbf {r}$. So I introduced a new convention $\mathbf {r} '=\mathbf {r} -\mathbf {l}$ similar to the original, to alter the content minimally.

(I'd be happy to explain why it's the displacement vector and not the parameter vector that appears in the integrals and expressions, but the text already said this, it just wasn't reflected in the formulas.)

However, $\mathbf {r} '$ was already used in the proof section for the line integral element. Apart from conflicting with the new notation, this was already inconsistent with all formulas above, which used $\mathbf {l}$, so I changed this to use the existing convention, but maintain the explicit difference ($\mathbf {r} -\mathbf {l}$) which, I agree, is probably clearest (rather than using the displacement vector throughout).

If anyone has any concerns with this, please feel free to leave a reply (and to message me directly if I don't respond promptly).

--RProgrammer (talk) 17:08, 20 March 2015 (UTC)

Excuse me, but authors and editors should stop acting as if the entire world has advanced math training and understands what they are saying. This article is just another example of articles that are too technical and not at all user-friendly.

For instance, what does the quantity "r'= r-1 " even mean?. What exactly are you subtracting "1" for and from what and what does "1" represent? A specific unit? A meter? A centimeter? What does "r" exactly mean and what is its physical meaning? And how "r'" fits in the equations? If anyone takes the time to answer, please consider that you are not addressing only professionals and that the answers to such questions may be self evident to you but not to everyone else, and that these things should be explained IN the article. Thanks. — Preceding unsigned comment added by 2A02:587:4507:1B00:BC0F:9D45:251:B361 (talk) 20:13, 10 July 2017 (UTC)

That's a lower-case L. Unfortunately it looks like a 1. I agree that we should avoid using lower-case L (l) for that reason.

Maybe we should replace it with $\ell$? I just looked it up, and it does have a boldface: $\ell {\text{ vs }}{\boldsymbol {\ell }}$. Any objections to switching the article from l to ${\boldsymbol {\ell }}$?

Sorry if the article is too technical. Remember, the people reading your post are not necessarily the same people who wrote the article. We're all busy people, but we can improve it bit by bit. What you said is helpful, and if you say what else is especially confusing, we can try to fix that too! The more specific you are, the easier it will be for me or whoever tries to improve it. :-D --Steve (talk) 21:38, 10 July 2017 (UTC)

Whadup, changed the variable names from $l$ to ${\boldsymbol {\ell }}{\text{ and }}\ell$. Sebastian tilman (talk) 13:01, 10 December 2017 (UTC)

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An upgraded image you might wish to use

Shown are the directions of $Id{\boldsymbol {\ell }}$, $\mathbf {\hat {r}}$, and the value of $|\mathbf {r} |$ in the integrand used to evaluate $\mathbf {B} =\int d\mathbf {B}$

This article might be too high-level for this image, but I just made it for Wikiversity formula sheet.--Guy vandegrift (talk) 00:21, 28 February 2018 (UTC)

Nice! I'd be happy if you posted it. (But the caption should be written in English.) --Steve (talk) 20:49, 28 February 2018 (UTC)

The quantity in the denominator should be absolute value squared.Constant314 (talk) 21:08, 28 February 2018 (UTC)

Thanks for taking it. It's yours to edit as you please. I will get back to wikiversity:OpenStax equations/University physics/V2.--Guy vandegrift (talk) 01:27, 1 March 2018 (UTC)

I brought it back. r and r-hat need to be r' and r'-hat to agree with the text.

Shown are the directions of $Id{\boldsymbol {\ell }}$, $\mathbf {{\hat {r}}'}$, and the value of $|\mathbf {r'} |$

Constant314 (talk) 01:40, 1 March 2018 (UTC)

I need the vector arrow symbols for OpenStax. Also, it would not be easy to create bold-faced symbols on Inkscape. But I can place a variation of the image with primes on commons for this article. Would adding primes but keeping the vector symbols be OK? --Guy vandegrift (talk) 02:32, 1 March 2018 (UTC)

Not sure what you mean about the vector symbols, but I think they are OK, if you mean what I think you mean.Constant314 (talk) 02:40, 1 March 2018 (UTC)

@Constant314: is this better?

No prime on the l or the B. Constant314 (talk) 03:39, 1 March 2018 (UTC)

 Done--Guy vandegrift (talk) 04:21, 1 March 2018 (UTC)

I see that you went with underscores instead of arrows. Its definitely not standard. The arrows are optional, but the underscores are a problem. Can you remove them? Constant314 (talk) 04:56, 1 March 2018 (UTC)

When doing calculations by hand the underscores are great because they are quicker and take less space. They also let you write rank-2 tensors by using two underscores. But I will remove them.--Guy vandegrift (talk) 06:15, 1 March 2018 (UTC)

I just discovered that there is a way to boldface the ell. It is a unicode character that Inkscape can render as an object that can have a border.---Guy vandegrift (talk) 06:43, 1 March 2018 (UTC)

I believe that's it. I'll look at it again tomorrow. Constant314 (talk) 07:07, 1 March 2018 (UTC)

Formulation of Biot-Savart law for vortex segments of finite length unclear, probably wrong

I believe that this remark "where A and B are the (signed) angles between the line and the two ends of the segment" is not correct. A and B should be the (signed) angles between the (vortex) line segment and the connection lines from the segment ends to the point (at which the induced velocity is calculated). This is not what is now stated. I recommend to check this. — Preceding unsigned comment added by Rschmehl (talk • contribs) 07:14, 7 November 2018 (UTC)

Alternate Representation

The Biot-Savart law presented here is an integral. But the way I learned it, the integral was derived from a simpler expression of the law in its differential form: $d\mathbf {B} (\mathbf {r} )={\frac {\mu _{0}}{4\pi }}{\frac {I\,d{\boldsymbol {\ell }}\times \mathbf {r'} }{|\mathbf {r'} |^{3}}}$

(Actually, the professor didn't express it in vector form, so it was more like this: $dB(r)={\frac {\mu _{0}}{4\pi }}{\frac {dI}{r^{2}}}$ I think he did it this way so it looked more like a familiar inverse square law. So I'm guessing I got the vector form right.)

I wonder if it would make sense to present the differential form first, then show what the derived integral looks like. If not, I think it still makes sense to present the differential form somewhere. –MiguelMunoz (talk) 11:11, 23 June 2020 (UTC)