How to Recognize Split Electric Fields - Comments

[etotheipi]

I'm going to go out on a limb here and just say that I don't think it then makes sense to decompose the electric field inside an inductor. You must either get two conservative fields, or two non-conservative fields (so any talk of a Helmholtz decomposition is out of the question). Of these two choices, both can produce a non-zero closed curve line integral due to the fact the domain is not simply connected. However, these don't make much sense in this context.

Feynman's treatment is the only one I've come across that I understand. I am done messing around with these unphysical splits

 

[Charles Link]

Well, it certainly isn’t as straightforward as it seems since the straightforward analysis for a battery leads to an inconsistent set of equations.

In any case, if what he is describing is not a Helmholtz decomposition then I am exceptionally skeptical of its validity. A much more rigorous treatment is required

Even for the inductor, I don't believe it is a Helmholtz decomposition. It seems to be in the category of a mathematical construction, with the $E_s$ well-behaved and following the rules of electrostatics, (e.g. $\oint E_s \cdot dl=0$), while the EMF's and the associated $E_m$'s, where $\mathcal{E}=\int E_m \cdot dl$, are basically a very different animal.

 

[Dale]

Even for the inductor, I don't believe it is a Helmholtz decomposition. It seems to be in the category of a mathematical construction, with the $E_s$ well-behaved and following the rules of electrostatics, while the EMF's and the associated $E_m$'s, where $\mathcal{E}=\int E_m \cdot dl$, are basically a very different animal.

Then I think some mathematical rigor is necessary. E.g. a definitive formula for calculating these split fields in terms of standard EM quantities. Otherwise any discussion requires consulting an oracle to determine the decomposition

If it is not a Helmholtz decomposition then the only other thing I could see is that it is the decomposition $E_s=-\nabla \phi$ and $E_m= -\frac{\partial}{\partial t} A$ where $\phi$ and $A$ are the scalar and vector potentials in the Coulomb gauge. But who knows, it certainly isn’t described here with enough rigor to say.

 

[Charles Link]

Then I think some mathematical rigor is necessary. E.g. a definitive formula for calculating these split fields in terms of standard EM quantities. Otherwise any discussion requires consulting an oracle to determine the decomposition

It seems to be a model that some like and others don't. In the case of an inductor, there is sufficient symmetry that $E_m$ can be computed. For a battery, such symmetry is absent, and it becomes a somewhat abstract description. It doesn't have tremendous mathematical rigor in that sense. You can postulate $\mathcal{E}=\int E_m \cdot dl$ for some $E_m$, but you can't measure the $E_m$ because it is always offset by a $-E_s$. Personally, I see some merit in the description, but others seem to find it to be lacking in fundamental soundness.

 

[hutchphd]

I do see some merit to @rude man 's approach.

What is the merit? Please be specific.
The open circuit electric potential of a battery is a fixed number, and that is well known and is very useful.
To infer, from that single fact, that there must exist an internal electric field Em (m is for magic) is, charitably, an interesting conjecture. It neither simplifies the circuit analysis nor elucidates any actual underlying physics.
Please can we please stop discussing Chimera. I am certainly finished.

 

[rude man]

Well, (98.2) didn’t come from me. That was from @rude man. It is clear that he will need to discard at least one of those equations in (98.1-6), but I am not sure which he will choose.

I am deliriously happy with 98. 1-6.

BTW 98.3 is a vector addition so $\bf E_s + \bf E_m = 0$ in coil (or battery or ...).
$\bf E_m$ points - to + in battery, $\bf E_s$ points + to - in & outside battery.
|$E_s$| = |$E_m$| in battery or coil wire.
No inconsistency, no sale.

 

[Dale]

I am deliriously happy with 98. 1-6.

Then you have discarded mathematics

 

[Charles Link]

@rude man Clearly 98.2 is incorrect. You do not have $\nabla \cdot E_m =0$ for the $E_m$ that your model gives. I think posts 124 and 125 kind of summarize the general consensus of this methodology.

 

[rude man]

@rude man Clearly 98.2 is incorrect. You do not have $\nabla \cdot E_m =0$ for the $E_m$ that your model gives. I think posts 124 and 125 kind of summarize the general consensus of this methodology.

$\nabla \cdot \bf E = 0$ for ANY electric field. Just ask Maxwell.

 

[rude man]

Then you have discarded mathematics

OK.

 

[Dale]

OK.

With that I think we are done here. There is no point in discussing something that is knowingly so diametrically opposed to all of physics since Newton’s day. This is a very disappointing outcome for this thread.