# Faraday's Law - When do we know when it is a motional EMF or an induced electric field?

So from what I know, Faraday's law states that when there is a change in magnetic flux, an EMF is induced.

This can be explained with motional EMF where when the magnet moves towards the conducting loop, in the reference frame of the magnet, the conducting loop is actually moving towards it. Hence, motional EMF can be applied where the magnetic force causes the charges to move, hence EMF is induced.

However, there is also the explanation of changing magnetic fields induces non-conservative curling electric fields according to Maxwell's equations, hence when there is a conducting loop, this induced electric field causes a the charges to move, hence EMF is induced.

My question is, how can we differentiate these 2 completely different scenarios from each other? Or are they the same scenarios?

They're essentially different scenarios having the same explanation to them. According to Lenz's law, the induced current produced in a circuit always flows in such a direction that it opposes the change or cause that produced it. The change referred to here is a change in the magnetic flux.

Now, when we consider the motional EMF case, the magnet moving towards the loop causes an increase in the magnetic flux passing through the loop. So naturally, a current is induced that opposes this change (kind of like inertia). Now, it's important to note that in this case too, induced electric fields are produced. This can be explained by the fact that induced current is produced by nothing other than induced electric fields, and hence, whenever there is induced current know that there exists an induced electric field in the same direction as the current at every point.

So, since both have induced electric fields, it's basically the same explanation.

• So is the induced current in the motional EMF due to induced electric fields or the magnetic force on the charges? Commented May 28, 2021 at 18:05
• The term 'magnetic force' is just a general way of referring to a force produced by a magnetic field. Search up 'Lorentz Force derivation' and you'll find how the expression $e=vcrossBdotl$ came into existence. Spoiler: it's caused by an induced electric field within the conductor. Commented May 28, 2021 at 18:09
• Oh my, thank you so much for clarifying my doubts! Commented May 28, 2021 at 18:14
• Hi, I can't find proof of how the e = bvl has anything to do with induced electric field. Could you direct me to your source? Commented May 28, 2021 at 18:26
• Oh, wait. I meant that motional EMF was caused by induced electric fields, which can be explained using Lorentz force. Ykw, I'll just explain it to you. Commented May 28, 2021 at 18:30

My question is, how can we differentiate these 2 completely different scenarios from each other? Or are they the same scenarios?

They are different descriptions of the same phenomenon, because they describe it in different frames of reference.

In the frame of the magnet, where the magnet is static and the wire moves, the mobile free charges in the wire experience electromotive forces due to rest of the moving wire, and these do work on the current; energy for this comes from the kinetic energy of the wire (or in case the wire is not slowing down, from the work of force maintaining its motion).

In the frame where the wire is static and the magnet moves, the current in the wire experiences induced electric field of the magnet. It does work on the current, and energy for this comes from the kinetic energy of the magnet (or in case the magnet is not slowing down, from the work of force maintaining its motion).