Is it just an experimental fact that changing magnetic flux through a loop induces current in the loop(Faraday's law) or could we explain it with some reasoning?

• What other kind of reasoning would you be looking for? You can build up fancier geometrical theories of electromagnetism, but when it comes to "how do we know that is true?", it comes down to the same experimental evidence that supports the simpler versions of the law. Commented Jun 1, 2017 at 21:59
• You may find this helpful: en.wikipedia.org/wiki/… Commented Jun 1, 2017 at 22:02

We can explain it easily if, in our frame of reference, the loop is moving and its motion makes the flux through it change. In that case the loop must be 'cutting flux'. As the loop moves the free electrons inside it move with it and experience motor effect forces (aka magnetic Lorentz forces $q\ \vec{v} \times \vec{B}$) as they are moving at an angle to a magnetic field. If you draw a diagram you'll see that there is a component of this force urging the electrons along the wire, so for each circuit of the loop the electron will have work done on it, i.e there is an emf in the loop.

When the loop is stationary and the flux through it changes (as for the secondary of a transformer with ac through its primary) an emf is induced in the loop, but this time it's not an obvious consequence of any 'more basic' law, unless we invoke the Principle of Relativity… It's clearly not the motor effect ($q\ \vec{v} \times \vec{B}$) force that operates because the charges aren't moving! Instead it is an electric field which acts on the charges and urges them round the wire. According to the Faraday-Maxwell law $$\vec{\nabla} \times \vec E =-\frac{\partial \vec {B}}{\partial t}$$To re-iterate, this is a law in its own right.

... that changing magnetic flux through a loop induces current in the loop(Faraday's law) ... could we explain it with some reasoning?

Properties of charges

Some electrons in metalls are bonded very week to the atoms and they can form a current. Electrons obey the intrinsic (ever existing) properties of electric charge and magnetic dipole moment.

People have learnt to scale this properties in the macroscopic scale. A potential difference is the separation of same charges in different places like in a capacitor. Connecting the two separated plates again together an electric current flows. Melting some materials - with existing but randomly distributed particles - to powder and pressing this powder in a strong magnetic field people made permanent magnets.

The interesting thing is that both phenomenons are not influencing each over directly. A motionless electron in a magnetic field doesn't moves to the magnetic poles, only the electron's magnetic dipole moment gets aligned. A motionless electron between two charged plates starts to move to a plate but it's magnetic dipole moment doesn't gets aligned.

Last not least than ever a charge gets accelerated this is accompanied by the emission of photons (electromagnetic quanta). This we have to remember for the understanding of the electromagnetic induction.

Requirements of electromagnetic induction

For the electromagnetic induction processes are needed two requirements to induce the third phenomenon:

1. Flow of charges (current)
2. Magnetic field
3. Acceleration of charges

Two of the three requirement are enough to induce the third and the positions are interchangeable:

1. Electric generator: A magnetic field (2) and the acceleration of charges (3) (in the winding of coils) induce an electric current (1).
2. Electric drive: An electric current (1) and the acceleration of the involved electrons in the coils (3) induce a magnetic field (2).
3. Lorenz force: A current (1) in a magnetic field (2) induce the acceleration of charge (3).

The process of EM induction

As it was said above an electric field doesn't influence a magnetic field and vis-a-vis. How than it's possible to induce

• with a current a magnetic field or
• with a magnetic field a current?

The natures trick lays in the emission of photons of accelerated charges and asymmetry of a magnetic dipole moment. The electric field of the electron -to some approxiamation - is symmetrically. The magnetic field isn't, it has poles. Moving into a magnetic field electrons have randomly distributed poles and this poles get aligned. Now the observed phenomenon of the emission of photons came into play. The photon emission disalign the pole's orientation again AND the - since the photon obey a moment - deflected the electron. Under the influence of a magnetic field the moving electron moves in tiny tangerine slices along a spiral path until they came to rest, exhausting their kinetic energy.

Now try to apply the above said to your knowledge about induction processes. If you found inconsistencies share your insights.