George Smyth XI

The Sequence for Maxwell's equations

I've put equations in "traditional" sequence not for sake of tradition, but for sake of symmetry: when you first see what is div E, and then you see div B, you are more likely to expect to see curl E next, not curl B. Chronology should be in the history section only, for readers interested in history of Maxwell's equations. Everything else should be physics presented in best way possible (and in many cases this way isn't chronological). --193.198.16.211 (talk) 10:22, 26 March 2008 (UTC)

I've labeled them by putting them in table. What do you think? --193.198.16.211 (talk) 10:55, 26 March 2008 (UTC)

Maxwell's equations

I've noticed that you have reverted one of my edits on Maxwell's equations article writing in your edit summary:

Actually, D corresponds to B, whereas E corresponds to H. B is the magnetic flux density, whereas H is the magnetic field strength. D and B are the weighted terms

Why would D correspond to B and E correspond to H? Names for B and H are just names and ones you mentioned are pretty old ones and not really used by physicists (see Magnetic field#cite note-4). And what do you mean by D and B being "weighted terms"? --193.198.16.211 (talk) 22:44, 2 April 2008 (UTC)

But today B is known to be more fundamental quantity than H and this is why in modern textbooks B is called the magnetic field.

And there are some reasons why E (not D) more closely parallels with B:

1. E and B both account for Lorentz force
2. E and B directly depend on total charge and current, while D and H directly depend on free charge and current. Moreover, to calculate E and B you need to multiply charges and currents by factor consisting of ε₀ μ₀, while to calculate D and H you need to use charges and currents "naked" without ε₀ μ₀
3. E and B are known to be more fundamental quantities than D and H respectively
4. Units of E and B and units of D and H differ by non-electromagnetic unit (one that can be expressed using only kilograms, meters and seconds)

So all of these reasons are suggesting that E corresponds to B , whereas D corresponds to H. --193.198.16.211 (talk) 17:09, 3 April 2008 (UTC)

As long as you know that D = εE and B = μH then you can use whichever of these expressions you wish in any of the equations of electromagnetism. You can write the Lorentz force as F/q = -gradΨ -(partial)dA/dt + μvXH if you so wish, just as Maxwell did. Or indeed as D = -εgradΨ -ε(partial)dA/dt + (1/c^2)vXH. George Smyth XI (talk) 11:07, 4 April 2008 (UTC)

F/q = -gradΨ -(partial)dA/dt + μvXH is impractical to use general materials since μ can be very complicated function. (see Maxwell's equations#Constitutive relations) while F/q = E + vxB is far simpler since you don't have to use μ, differential operators and potentials - only E, B and v are used. Just because Maxwell did something the way he did it doesn't mean that his way is the best. After all, he did it At least 100 years ago, today we understand it better than he did.

And also, B is today known to be more fundamental than H, just like E is known to be more fundamental than D. --193.198.16.211 (talk) 11:21, 4 April 2008 (UTC)

The -gradΨ -(partial)dA/dt bit was totally irrelevant to the issue being discussed. So I'll repeat myself again using E in the Lorentz force. We can write the Lorentz force as either F/q = E + vxB or as F/q = E + vxμH. I didn't express a preference one way or the other.

And it's not an issue of which is more fundamental. The idea that B coresponds D stems from the fact that B = μH and D = εE.

Also, you say that today we know alot more than Maxwell. I very much doubt that.George Smyth XI (talk) 11:32, 4 April 2008 (UTC)

Faraday's law

Hi George:

Sliding loop in stationary homogeneous B-field

Thanks for the comments. I think I got it. It's all related to Leibniz_integral_rule#Multidimensional_form, which somehow got deleted earlier from the Faraday page.

I've been trying to use the flux rule with distributed current paths, like the sliding loop pictured here. It seems the flux law is easiest to use in these situations where there is a distributed portion of the current path by thinking of the cutting of flux lines rather than the actual flux - the change in flux area is easier to imagine than finding the area and then taking a derivative. When the sliding loop is a solid plate, or in the case of the Faraday disc generator with a solid disc, this idea of the change in linked area is just as easy to use as the Lorentz force law and a lot easier than trying to find the total flux through the circuit (which requires figuring out what on earth the current is doing inside the distributed portion of the path; for example, how do you treat the two paths in the sliding loop of the picture?). What do you think about flux cutting as interpretation of the flux law, or how to treat the Faraday disc generator? I've implemented this at Faraday's law. Brews ohare (talk) 15:33, 20 April 2008 (UTC)

Brews, I would say that flux cutting is purely related to the vXB effect. It occurs when a charged particle moves at right angles to Faraday's tubes of force. Ie. when it moves across their cross section.

The (partial)dA/dt effect is a time dependent thing. It's very hard to know for sure what the exact microscopic mechanism for this is inside Faraday's lines of force.

They are both catered for by the flux law. The vXB term is catered for by the convective aspect, and the other term is catered for by the partial time derivative aspect.

See if you can dig up that paper in the January 1984 Toth Maatian Review. It's about the Lorentz force and Maxwell's equations and total time derivatives. I don't have a copy here.George Smyth XI (talk) 06:23, 24 April 2008 (UTC)

Lorentz force

Hi George: See if you want to comment upon Lorentz force. Brews ohare (talk) 02:34, 21 April 2008 (UTC)

Faraday paradox

George: I have made a number of changes here. You might want to comment. Brews ohare (talk) 18:47, 23 April 2008 (UTC)

Leibniz rule

Hi George: I posted a request for Stevenj to look into the integration business, Leibniz rule of integration, per your suggestion. Thanks, Brews ohare (talk) 16:10, 24 April 2008 (UTC)

Moving magnet and conductor problem

I've rewritten the intro to moving magnet and conductor problem. Having done that, I'm left feeling that the use of A is a much better approach than the E and B method, because E and B introduce the false dichotomy between electric and magnetic fields, mainly due to lumping the solenoidal and conservative E-fields together. These two components of E-field should be kept separate, as they have different origins and different behavior under switching of frames of reference. A cleaner formulation would leave out B-field and refer instead to A-field, while E--field would refer only to the conservative E--field. Of course, the gauge-transformation freedom makes you think that the potentials aren't "real", but one could argue that the E- and B-fields aren't real either - it's only forces and currents that matter. Differently put, we'd have the E-field redefined as only the conservative part and redefine the B-field as B = −∂ _t A + v × curl A . Would that fly better? (I'm not suggesting Wiki be rewritten like this, just thinking out loud.) Brews ohare (talk) 13:11, 2 May 2008 (UTC)

Invitation

I invite you to read my comment (No. 48) to "Faraday's Law of Induction." Mike La Moreaux (talk) 02:25, 13 September 2009 (UTC)