# Why does electromagnetic induction actually occur?

In my book, it is written that "An emf is induced in a loop when the number of magnetic field lines that pass through the loop is changing" (Faraday's law)

I understand that whenever there is a change in magnetic flux, there will an emf induced in a loop and this in turn will induce a current.

However, I really want to understand what exactly goes on to cause this. I just want to check if I am right:

1. There is a relative movement between the loop and the magnet (e.g. loop moving towards magnet)

2. Thus, electrons in the loop are "moving" relative to the field

3. A moving charge experiences a force perpendicular to the direction of the field

4. As a force is exerted on the electrons, they move in a particular direction

5. Current is induced

I do not know much calculus and studying high school physics but could someone please help me get an intuition behind Faraday's law or tell me if my way of thinking about it is right?

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excellent question! –  flies Mar 3 '14 at 14:26

## 2 Answers

You are correct. Essentially it all boils down to the Lorentz force $\vec{F} = q(\vec{E} + \vec{v} \times \vec{B})$. If you move into a frame of reference where the section of the loop is momentarily stationary, then you can do a Lorentz transformation to find out what $\vec{E}$ is in that frame. In that frame, $\vec{v}=0$ of course, so the second term is zero, but $\vec{E}$ will now be non-zero, and, in fact, equal to $\vec{v}\times\vec{B}$. In this frame, the force on the charges is purely electrical in nature, i.e., due to an electric field, and this is why you can define an EMF analogously to electric potential. But because wires are usually loops and each segment of the loop has it's own reference frame, there's no way to do this everywhere (globally).

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I did not learn about Lonrentz force or reference frames yet but thank you so much for assuring me that my intuition behind Faraday's law is correct. –  Eliza Nov 8 '13 at 6:22
What does your intuition say about a permanently magnetized cylinder of iron spinning about its axis (which is also it's magnetization direction). Is there an EMF produced? –  lionelbrits Nov 8 '13 at 14:06
Is the iron spinning inside some kind of coil or do you mean if an emf is induced in the cylinder itself? –  Eliza Nov 8 '13 at 14:38
I chose iron because it is conductive, so I mean the cylinder itself. –  lionelbrits Nov 9 '13 at 12:01
hmm...this is the picture in my mind: the electrons of the iron are following a circular path when the cylinder rotates, but the electrons will not be "moving" relative to the field because the fields are "moving" too... my intuition tells me that there is no emf induced –  Eliza Nov 9 '13 at 13:28

The important thing to understand here is (sorry to start out with the obvious), that electricity and magnetism are the same force. That is to say, electrons in a wire will feel a force when subjected to a magnetic flux, as electrons are essentially small magnetic dipoles themselves. This force creates an electric field, and because the electrons are charged, a current will begin to flow.

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Well, considering that electrons are the unit of charge I wouldn't say that they're just magnetic dipoles... I think that is more correct to say that a moving charge radiates energy in the form of electromagnetic fields. In this sense it's absolutely correct to say that electricity and magnetism are the same force –  Mattia Nov 9 '13 at 16:10
The point I was making is that electrons have spin, and therefore have a magnetic dipole moment. An electron can therefore be considered (in very simplistic terms!) to be a small magnet. Electrons are certainly not just magnetic dipoles, sorry for not making that clearer –  Angelo Nov 9 '13 at 16:28