# An Interesting Question on Faraday's Law of Electromagnetic Induction

• Narayanan KR
In summary: AC currents or power generation.In summary, the Faraday shield concept states that charges inside a cage are shielded from external influences, but the cage itself is still affected by external charges. Additionally, shielding is not perfect and even in a superconductor there is a skin depth where external fields decay. However, even with a small skin depth, there are still surface charges and currents. While shielding is important for determining the best conductor geometry, it does not prevent AC currents or power generation.
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 ?

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.

Narayanan KR said:
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.

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
kuruman said:
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?

mitochan said:
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

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}##

Narayanan KR
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.

Narayanan KR
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.

Narayanan KR and Dale
Narayanan KR said:
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.

SredniVashtar, vanhees71 and Narayanan KR
Dale said:
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...

Narayanan KR said:
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.

Last edited:
vanhees71 and Narayanan KR

## 1. What is Faraday's Law of Electromagnetic Induction?

Faraday's Law of Electromagnetic Induction states that when a conductor moves through a magnetic field or when there is a change in the magnetic field, an electromotive force (EMF) is induced in the conductor, resulting in the production of an electric current.

## 2. Who discovered Faraday's Law of Electromagnetic Induction?

Michael Faraday, a British scientist, discovered the law in the 1830s through his experiments with electricity and magnetism.

## 3. How is Faraday's Law of Electromagnetic Induction used in everyday life?

Faraday's Law of Electromagnetic Induction is used in many everyday devices, such as generators, transformers, and electric motors. It also plays a crucial role in the production of electricity in power plants.

## 4. What is the mathematical equation for Faraday's Law of Electromagnetic Induction?

The mathematical equation for Faraday's Law of Electromagnetic Induction is:
EMF = -N(dΦ/dt)
where EMF is the induced electromotive force, N is the number of turns in the coil, and dΦ/dt is the rate of change of magnetic flux.

## 5. What are some real-life applications of Faraday's Law of Electromagnetic Induction?

Faraday's Law of Electromagnetic Induction has various applications, including power generation, wireless charging, electromagnetic braking, and induction heating. It is also used in medical devices such as MRI machines and in the production of electronic devices like speakers and microphones.

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