Is Faraday's law applicable on a lesser scale?

[radaballer]

Farraday's law tells us a magnet traveling through a solenoid will induce a current. It is understood electromagnetic properties and magnetic properties are somewhat interchangeable, and this allows magnets to move electrons in the wire. Can it then be inferred that an electron moving through a solenoid (a much smaller one) would cause an induced EMF.

 

[Khashishi]

Electric and magnetic fields aren't quite interchangeable, although they are both parts of the electromagnetic field. You have to understand Maxwell's equations to see their connection.

An electron moving through a solenoid will cause an induced EMF, because a moving charge generates a magnetic field. There are a couple equivalent ways of thinking about this. The moving charge is a current, and the current creates a magnetic field which is changing as the current shifts. Or, in the frame of reference of the electron, it creates an electric field. In the frame of reference of the solenoid, the electric field is transformed into an electromagnetic field via a Lorentz transform, and the magnetic portion interacts with the solenoid.

 

[radaballer]

Thank you Khashishi

 

[Grigori Saiyan]

Farraday's law tells us a magnet traveling through a solenoid will induce a current. It is understood electromagnetic properties and magnetic properties are somewhat interchangeable, and this allows magnets to move electrons in the wire. Can it then be inferred that an electron moving through a solenoid (a much smaller one) would cause an induced EMF.

The Faraday's law should be working at least within the scale where electrodynamics is applicable - up to classical radius of electron (r_e)

r_e = e²/mc²
where e - electric charge of an electron, m - its mass, and c is the speed of light. The magnitude of the scale is approximately one fermi. This is a rather fundamental aspect of the question than practical.

Grigori Saiyan

 

[Khashishi]

You can't make a solenoid that small anyways.

 

[Grigori Saiyan]

Yes, of course. That's why I am saying this is just a formal aspect, but not practical one. Faraday's law has been discovered with the use of solenoidm, but its vey meaning is in generating spatially-varying electric field induced by a time-varying nagnetic field and vice versa (reflected in one of Maxwell equations). Sources and scales of electric and magnetic fields depend on situations