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Although, it seems very easy to find the magnetic field produced by a solenoid or a toroid, all we got to do is to make a suitable an Amperian Loop and take the $\mathbf B$ out of the integral and so on.

But the main step is to find the direction of magnetic field. For example see these derivations of Griffiths:

Toroid 1.

Toroid 2

I want to know who actually drived those equations, who actually worked out for the directions of magnetic field (Griffiths has done his)?

I searched for magnetic field by solenoid and toroid but found nothing historical. I aimed at finding something from Wikipedia’s “Refernces” or “External Links”. I read somewhere that Wilhelm Eduard Weber did work out the field for some geometrical shapes.

So, I request for some refernces where I can find the actual derivations of magnetic field produced by solenoid and toroid.

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  • $\begingroup$ Hm? At some point the community settled on a defined "direction," similar to defining the cartesian 3D coordinates via the "right-hand rule." Are you looking for something more? $\endgroup$
    – Carl Witthoft
    Mar 23, 2020 at 12:41
  • $\begingroup$ I found that it was Pierre De Laplace who actually worked out the magnetic fields not Mr. Biot or Mr. Savart. I found it Greiner’s book on EM. $\endgroup$
    – Knight wants Loong back
    Mar 23, 2020 at 13:11

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