I Magnetic Field of a Moving Charge and the Displacement Current

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I would say the equation in the yellow box is simply wrong. The Biot-Savart law applies to steady currents, and a single moving charge is not a steady current.

But, perhaps, some texts tend to gloss over this?
I think almost every introductory textbook uses that equation.
 
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I think almost every introductory textbook uses that equation.
Unfortunately introductory textbooks in physics do leave some issues either not explained, or actually wrong and corrected later. Its a while since I read introductory EM textbooks so I cant comment (my first was from Wiley and is now falling to pieces). Feynman is usually reliable, but as just about everyone notes is not the best actual textbook - but just about always recommended as supplementary reading. It is the book for those not necessarily interested in doing well on tests, but in understanding physics.

Later you will likely study Jackson, but I humbly recommend of course Feynman (which is available free, but I purchased the books myself) and Schwinger's book:
https://www.amazon.com/dp/0738200565/?tag=pfamazon01-20

IMHO Schwinger is better than Jackson, and I would get a copy purely for reference. It is always my go-to book on EM. Don't worry that its graduate level and you quite likely are not. That's the purpose of reference books - they become your go-to book not just for refreshing your knowledge of things, but at first while you do not get their full impact - you understand it - but its full value comes later after a number or readings over many years. For Classical Mechanics Goldstein in usually recommended for that like Jackson for EM - but IMHO Landau - Mechanics leaves Goldstein for dead. Landau - Classical Theory Of Fields is also excellent - but IMHO Schwinger is better - which is saying something since I practically worship Landau. Schwinger seems to combine the best of Jackson and Landau (the issue with Landau is he is quite terse).

Thanks
Bill
 
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I agree with you, but it is like a morning stroll to read Feynman. And I always learn something

Feynman is usually reliable
For the record I will presume to summarize to the extent that he does derive the "Biot-Savart" result for a point charge rigorously in the non-retarded time limit by transforming the fields.
 
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I agree with you, but it is like a morning stroll to read Feynman. And I always learn something.
Feynman is like that, as well as Landau. Which is why I got both for reference purposes. Schwinger is like that in spades. Its just that personally I mined EM to my satisfaction ages ago.

Thanks
Bill
 
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Schwinger is like that in spades.
I need to get a copy and look at it again....never had it for a course. I did teach an undergrad course using Griffiths and found it very good as a textbook.
And Jackson is, well, Jackson........not my favorite but not really replaceable either.
 
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@bhobba @hutchphd @PeroK thanks guys, I was checking out Jefimenko's equations, and they obscure the symmetry between the E and B fields.
There are no magnetic monopoles or magnetic currents.

But even without magnetic monopoles, the symmetry can be clearly seen in Maxwell's equations.

So, do you know of any formulas for the E and B fields which both use retarded time and show the symmetry between them?
 

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