Is Feynman's "flux rule" a popular name?

[sweet springs]

Feynman　in 17–1　The physics of induction　http://www.feynmanlectures.caltech.edu/II_17.html explains Faraday's law and flux rule the latter of which include motion effect of circuit. Is the name flux rule a popular one ? Does it have more formal name? I wonder if it is sometimes called also Faraday's rule though I think we should distinguish them.

 

[jtbell]

Griffiths also uses the term "flux rule" in his textbook. He first introduces motional EMF in a constant (with respect to time) B field, and the flux rule. Then he introduces the EMF induced by a time-varying B field, notes that one can use the same flux rule to calculate the EMF in these cases, and explains them in terms of an induced E field. He uses "Faraday's Law" to refer only to these cases.

 

[sweet springs]

Thanks. I am happy to know that Feynman is not alone.

I think flux rule contains more than Maxwell's $\nabla \times E=-\frac{\partial B}{\partial t}$. Is that right?
Faraday's law is equivalent to Maxqwll's $\nabla \times E=-\frac{\partial B}{\partial t}$. Is that right ?
I am still confused.

 

[jtbell]

I think flux rule contains more than Maxwell's $\nabla \times E=-\frac{\partial B}{\partial t}$. Is that right?

Correct.

Faraday's law is equivalent to Maxqwll's $\nabla \times E=-\frac{\partial B}{\partial t}$. Is that right ?

Correct.

I am still confused.

How, exactly?

I will guess that it might help to consider the integral form of Faraday's law: $$\oint {\vec E \cdot d \vec l} = - \frac {d} {dt} \int {\vec B \cdot d \vec a}$$ In applying Faraday's Law strictly, the path of integration on the left side, which is of course also the boundary of integration on the right side, must remain fixed in space, in the inertial reference frame that we are working in. In this case there does not need to be a physical conductor (wire) along that path. The induced $\vec E$ field exists regardless.

If we do have a (stationary) wire along the path, the induced $\vec E$ exerts a force $\vec F_e = q \vec E$ on the charge carriers in the wire, which produces an emf along the wire.

If the wire is moving in our inertial reference frame, then in addition to the above, we have a magnetic force on the charge carriers: $\vec F_m = q \vec v \times \vec B$. This produces an additional emf along the wire.

The flux rule gives the total effect of the electric and magnetic emf's around a closed loop.

 

[sweet springs]

Thanks for your clear reply. Just one thing to confirm

The flux rule gives the total effect of the electric and magnetic emf's around a closed loop.

Loops of Faraday's law are not limited to real circuit at all, but closed loop in the flux rule is real circuit where charge carriers are under effect of electric and magnetic emfs.

 

[sweet springs]

And as Feynman pointed out, the material of the circuit remains the same.

 

[vanhees71]

Thanks. I am happy to know that Feynman is not alone.

I think flux rule contains more than Maxwell's $\nabla \times E=-\frac{\partial B}{\partial t}$. Is that right?
Faraday's law is equivalent to Maxqwll's $\nabla \times E=-\frac{\partial B}{\partial t}$. Is that right ?
I am still confused.

The point is that most textbooks confuse the subject by not clearly stating that the naive "flux rule" holds true only if the surface and its boundary you integrate Faraday's Law (in SI units ;-)),
$$\vec{\nabla} \times \vec{E}=-\partial_t \vec{B},$$
over is at rest. Then and ONLY Then you have
$$\int_{\partial f} \mathrm{d} \vec{r} \cdot \vec{E}=-\frac{\mathrm{d}}{\mathrm{d} t} \int_{f} \mathrm{d}^2 \vec{f} \cdot \vec{B}=-\frac{\mathrm{d}\Phi}{\mathrm{d} t}.$$
If you have the general case of a moving surface and boundary, you get an additional term when bringin the partial derivative wrt. $t$ out of the integral, which you can lump to the left-hand side, leading to the complete and correct electromotive force:
$$\int_{\partial f} \mathrm{d} \vec{r} \cdot (\vec{E}+\vec{v} \times \vec{B})=-\frac{\mathrm{d}}{\mathrm{d} t} \Phi.$$
In any case it's more save to stay with the fundamental laws, which are the local Maxwell equations, including the relativistic (!) constitutive equations (in the most simple approximation you may use the linear-response approximation a la Minkowski). Then and only then everything is consistent and frame independent, as it must be.

Nevertheless particularly this chapter of the Feynman Lectures vol. 2 is a gem of textbook literature and should be carefully studied by any serious physics student!