Question

What is the quantity associated with the Ampére-Maxwell Law
\[\oint_C\mathbf B\cdot\mathrm d\boldsymbol\ell = \mu_0^{}I+\mu_0^{}\varepsilon_0^{}\frac{\mathrm d \Phi_E}{\mathrm dt}\]

Answer 1

Units are
webber per metre, or tesla meters
\[\qquad[\tfrac{\text{Wb}}{\text m}]\qquad\text{ or }\qquad[\text T\cdot \text m]\]

Answer 2

How about Newton/ampere

Answer 3

Are you referring to the displacement current ?

Answer 4

No the actual current as would be from the term\[\mu _{0}I\]

Answer 5

Sorry, I was trying to clarify the original question - all the terms have to have the same dimensions or the equation would be nonsense.

Answer 6

Faraday's Law of Induction

\[\mathcal {E}=\oint_C\mathbf E\cdot\mathrm d\boldsymbol\ell = -\frac{\mathrm d \Phi_B}{\mathrm dt}\]

Is a quantification of electromotive force (EMF).


Is the some concept like a magnetomovitve force that is the quantity of Ampére-Maxwell Law? Something that means the sum of the enclosed current and displacement current, but also has the \(\mu_0^{}=4\pi\times10^{-7}[\text T\cdot \text m/\text A]\) factor?

Answer 7

Yeah whenever I think of anything at all like this I can't really quite say I understand it. I mean when it comes down to it, what _is_ energy or momentum? They sort of are what they are, even though it feels like a tautology. It's just a way of shortening the statement that the product of an objects velocity and mass are conserved we can say their momentum is conserved.

I think your analogy of the magnetic field to voltage is pretty good, since it does come up as V*m and this idea translates pretty well to T*m. Although there is probably a better way to think about it, I just imagine it as something like momentum in that it's just sort of conserved no matter how we move around a wire in the path of a single closed loop we will always get the same value for the product of these two things.

I don't know, maybe that's just how it is and there's nothing deeper we can do about it. It seems pretty straightforward, and doesn't really have a name that I know of, but we can observe it to be true. I wish I could help more, but you might find it interesting that Clifford Algebra condenses all 4 maxwell equations into a single equation. I've also heard something about how the magnetic field is something like a relativistic lagging of the electric field or something weird I don't understand so maybe if you study more you can explain it to me and maybe it all makes more sense the deeper you go in haha.

Answer 8

Magnetomotance does in fact have a unit. It is the Gilbert and is equivalent to an ampere.

1 Gilbert (Gi or Gb) = .79577... amperes.

You should divide your equation by u0 to get the correct definition of magnetomotance.

Answer 9

i.e. \[\frac{1}{\mu _{0}}\oint B\cdot dl= magnetmotance\]