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I was reading about the Faraday Law, and there is one thing that is not clear to me.

If we have a wire loop, and we change the magnetic flux that passes through the surface that this wire encloses, whether because of the magnetic field changes over time or the surface enclosed changes, or both, we will have induced current in the wire. And if we are having a current, then the charges are moving along the wire,something which happens when there is an electric field. Since the charges (electrons) move constantly, then the E-field should be there all the time, and that can be possible when we have a potential difference, in other words we should have two points in the wire, that establish this potential difference. This much I understad, but I have two questions:

  1. How exactly we gain this induced current? I understand that the magnetic flux change is the cause, but what happens inside the wire, what happens with the free carrier, how is the change of flux related to the existence of a force inside the wire loop, that causes the movement of the charges?

  2. If in the wire we have this electric potential difference, then as I said, we should have two points along it, where we have two differen values of the electric potential, and that's the potential difference or the voltage. How do we find these two points? Or it doesn't matter?

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First of all, An EMF doesn't have to be an electric field, It only is required that Work is being done on an object travelling in a certain path .

When there is a changing magnetic field, there is an induced electric field,

When there is a changing surface, because particles in the wire are in the presence of a magnetic field, they will experience a force q$ \vec{V} × \vec{B} $ This force is the cause of the EMF when the magnetic field is unchanging

Faradays law states the EMF about a CLOSED path, meaning your starting point A and final point B are the same point.

Potential difference as a concept isn't defined for faradays law as the field is non conservative, meaning $ \int \vec{E} \cdot \vec{dl}$ is PATH DEPENDANT meaning the work done by the field on an object changes depending the path I take.

meaning I physically cannot define potential difference between 2 points as I need to know the path inbetween, easy to visualise

Imagine I go clockwise about my path, starting at A and finishing at A, it gives me some value.

Now if I go anticlockwise, I would get a different result as my field is in the opposite direction

Mathematically conservative field are in the form $\nabla V$ Which means the curl is zero, which isn't the case in faradays law.

$\int \vec{E} \cdot \vec{dl}$ js defined however.. Just for the specific path you take, which is a closed path

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