An Interesting Question on Faraday's Law of Electromagnetic Induction

[Narayanan KR]

On examining Maxwell's third equation which is about time varying magnetic fields (Faraday's electromagnetic induction) we find that time varying magnetic fields produce loops of electric fields in space irrespective of whether a coil is present or not, if any coil is present then these loops of electric fields are said to produce an induced emf in the coil as stated in Faraday's law.

But, every metal is a Faraday Shield i.e. it won't allow any electric flux to pass via it, then how come the electrons deep inside the coil wire be influenced by this induced electric field ?

Is there any involvement of Poynting Theory, where S = E X H energy diverges into surface of wire there by exciting electrons on the surface alone ?

 

[kuruman]

Electrons are affected in this case the same way they are affected when you establish a potential difference across the ends of a conducting wire using a battery: they flow.

 

[hutchphd]

Summary:: Time varying magnetic fields produce loops of electric fields, which are said to be responsible for induced emf in a coil of wire linked to that field, but how can these electric fields influence electrons inside a metal wire there by creating an emf, provided no metal allows electric fields through it ? i.e. they are basically Faraday shields.

But, every metal is a Faraday Shield i.e. it won't allow any electric flux to pass via it, then how come the electrons deep inside the coil wire be influenced by this induced electric field ?

Perhaps it is easier to posit that inside the metal are two countervailing fields that must add to zero. One is from the "external" sources and one is from the mobile charge. It is this response that produces the internal influence.

 

[mitochan]

When electric field generated from outside charges are applied to conductor, electrons in conductor move to surface so that applied field and generated field of their own cancel inside the conductor. If not canceled it means electrons inside the conductor still "feel" it and move to complete equilibrium. This is electrostatic shield.

In your case of inductance, moving electrons are in dynamic situation, they do not form such equilibrium positions and keep moving.

 

[Narayanan KR]

Electrons are affected in this case the same way they are affected when you establish a potential difference across the ends of a conducting wire using a battery: they flow.

Yes electrons flow if a wire is connected to a battery, but not due to coulombic forces pushing/pulling them, but due to electromagnetic energy S = E X H diverging into the surface of wire as stated by Prof Poynting and Heaviside right?

 

[Narayanan KR]

When electric field generated from outside charges are applied to conductor, electrons in conductor move to surface so that applied field and generated field of their own cancel inside the conductor. If not canceled it means electrons inside the conductor still "feel" it and move to complete equilibrium. This is electrostatic shield.

In your case of inductance, moving electrons are in dynamic situation, they do not form such equilibrium positions and keep moving.

So if I understand you and @hutchphd correctly, electrons in the wire move so as to attain equilibrium with external electric field at the surface, hence they keep moving

 

[hutchphd]

Yes but it is not a "momentum" effect.
The charges move because $\vec F=q\vec E$ and $curl \vec E=-\frac {\partial \vec B} {\partial t}$

 

[mitochan]

Another saying is there exists dead end or no for electrons. At dead end surface, accumulated electrons prevent other electrons to come by repulsive force. At last no more electron would come by full cancellation of field comes from outside source and the repulsive field from accumulated surface electrons.

 

[tech99]

The electrons only feel the effect when the magnetic field is changing, and in such circumstances we observe Skin Effect, where the electrons near the surface move and carry the current. Electrons deep in the metal do not carry the current.

 

[Dale]

Summary:: Time varying magnetic fields produce loops of electric fields, which are said to be responsible for induced emf in a coil of wire linked to that field, but how can these electric fields influence electrons inside a metal wire there by creating an emf, provided no metal allows electric fields through it ? i.e. they are basically Faraday shields.

This premise is fundamentally flawed.

First, the idea of shielding is that charges inside the Faraday cage are shielded from external influences. It does not say that the cage itself is unaffected. In fact, the cage is very much affected by the external charges.

Second, shielding is not perfect. Even in a superconductor there is a skin depth. This skin depth is the frequency-dependent depth at which an external EM field decays to 1/e of the surface value.

Finally, even if the skin depth were infinitesimal you would still have surface charges and surface currents.

Overall, the shielding effect does happen, but not the way you infer. It is important for things like determining the best geometry for the conductor, but it in no way prevents AC currents or power generation.

 

[Narayanan KR]

This premise is fundamentally flawed.

First, the idea of shielding is that charges inside the Faraday cage are shielded from external influences. It does not say that the cage itself is unaffected. In fact, the cage is very much affected by the external charges.

Second, shielding is not perfect. Even in a superconductor there is a skin depth. This skin depth is the frequency-dependent depth at which an external EM field decays to 1/e of the surface value.

Finally, even if the skin depth were infinitesimal you would still have surface charges and surface currents.

Overall, the shielding effect does happen, but not the way you infer. It is important for things like determining the best geometry for the conductor, but it in no way prevents AC currents or power generation.

It is not flawed but a contradiction that very few seem to have noticed, a perfect conductor is one that reflects EM energy and a perfect insulator is one that allows EM energy to pass via.
.
The Theory that electrons move inside solid wire should be called "Plumber's Electricity" as it uses analogy of water moving in a pipe and it's rudimentary explanation, I am sure you are aware of Prof Poynting's Theory that orthogonal E and B fields produce energy flow S = E X B parallel to circuit wire and some part of this energy diverges into every point in the circuit, however not all points receive equal potential V hence resulting in a potential difference.

I was genuinely looking for someone to give explanation to faraday's induction in terms of EM energy and it's divergence as I don't know how...

 

[Dale]

It is not flawed but a contradiction that very few seem to have noticed, a perfect conductor is one that reflects EM energy

Even a superconductor has a skin depth.