Confused about electromotive forces

[cianfa72]

TL;DR

About the role of electromotive force in Maxwell equations formulation

Hi,
reading Griffiths - Introduction to Electrodynamics I'm confused about his claims in section 7.1

In principle, the force that drives the charges to produce the current could be anything - chemical, gravitational, or trained ants with tiny harnesses. For our purposes, though, it’s usually an electromagnetic force that does the job. In this case Eq. 7.1 becomes $$\vec J = \sigma(\vec E + \vec v \times \vec B)$$

My point is that the job of electromotive force $f$ is actually produce the "movement/drift" of free charges against the electromagnetic field, so $f$ should not be given by the Lorentz force as in Eq. 7.1.

In other words the fields $\vec E$ and $\vec B$ entering in the formula above seem to be the "external cause" of current flux/current density $\vec J$ (through the Lorentz force acting on the free charges) when they are not.

 

[anuttarasammyak]

TL;DR Summary: About the role of electromotive force in Maxwell equations formulation

My point is that the job of electromotive force f is actually produce the "movement/drift" of free charges against the electromagnetic fields,

Electromagnetic field is defined as magnitude of force on unit charge there iwith speed. Is electromotive force which is "against the electromagnetic fields" in your point, not electromagnetic field force but another kinf of force ?

 

[cianfa72]

Electromagnetic field is defined as magnitude of force on unit charge there iwith speed. Is electromotive force which is "against the electromagnetic fields" in your point, not electromagnetic field force but another kind of force ?

Yes, that's my point. Take for instance a simple circuit with a battery and a load: the electromotive force $f$ inside the battery is due to chemical processes inside it.

What I think is the following: since the Lorentz force $F$ from the $E$ and $B$ fields acts on the charges, then, if we assume charges not accelerating w.r.t. an inertial reference frame, it follows that the electromotive force $f$ acting on them must be equal to the Lorentz force $F$ acting on them.

 

[anuttarasammyak]

Yes, that's my point. Take for instance a simple circuit with a battery and a load: the electromotive force f inside the battery is due to chemical processes inside it.

Though I don't have and have not read Griffith, I assume that your point is covered in eq. 7-1. Could you show it ?

 

[cianfa72]

Could you show it ?

Here the page, section 7.1

 

[anuttarasammyak]

Thanks. Saying “for our purposes” he excluded chemical which you mentioned, mechanical, thermal and other contributions from 7.1 and focusing remaining EM forces which is reduced to Ohm’s law. In my taste I would not like to say it electromotive force but say forces applying on charged particles or electrons in this context.

 

[pines-demon]

Obviously Ohm's law holds in metals, but any true justification has to come from a fully quantum-many-body theory when you show that you can neglect most (but not all of the interaction terms). The number of assumptions that a book takes in order to simplify it like that is not small.

 

[cianfa72]

Thanks. Saying “for our purposes” he excluded chemical which you mentioned, mechanical, thermal and other contributions from 7.1 and focusing remaining EM forces which is reduced to Ohm’s law.

Yes, but my point is: fields $E$ and $B$ that enter in the EM force given by Lorentz force equation in the form of Eq. 7.2 are to be understood as the "sources" of "other" EM fields.

In a sense those $E$ and $B$ are actually assigned and are the reason behind the electromotive force $f$ that acts on the charges inside the generator/battery.

Edit: I think this thread is related to my question too.

 

[anuttarasammyak]

Again I would like to draw your attention that chemical is not included in this page of Griffith. I expect that what you say for chemical battery, thermo-couple physics, and induction which is em force by EM are treated somewhere in later chapters. Please be patient for a while.

 

[TSny]

In section 7.1.1, Griffiths uses the symbol $\mathbf f$ to denote the net force per unit charge acting on the charge carriers at some point in a circuit. The term"electromotive force", $\mathcal{E}$, is not used in section 7.1.1. $\mathcal{E}$ is defined in the next section (7.1.2) in terms of a line integral of $\mathbf f$. $\mathbf f$ and $\mathcal E$ have different units. So, we should not refer to $\mathbf f$ as an electromotive force.

Section 7.1.2 might address some of your questions concerning the "sources" of the force per unit charge $\mathbf f$ acting on the charge carriers in the circuit.

 

[cianfa72]

In section 7.1.1, Griffiths uses the symbol $\mathbf f$ to denote the net force per unit charge acting on the charge carriers at some point in a circuit. The term "electromotive force", $\mathcal{E}$, is not used in section 7.1.1. $\mathcal{E}$ is defined in the next section (7.1.2) in terms of a line integral of $\mathbf f$. $\mathbf f$ and $\mathcal E$ have different units. So, we should not refer to $\mathbf f$ as an electromotive force.

Ah ok, now it makes sense. I had been confused from the statement about the type of forces that can drive the charges to produce current.