# Magnetic induction, Faraday's law and the likes

1. Mar 19, 2006

### vidmar

Recently I started "studying" electromagnetic induction (O.K. that might be a bit of an overstatement, but I am interested in it, so it's just as well) and I came to the following important "discoveries":
- one of the Maxwell's equations states (Faraday's law if my memory serves me correct) that given any fixed surface with its border, the voltage "induced" on this border (but more importnatly just the voltage in the sense of the integral of the electric field along this border) equals the negative time derivative of the magnetic flux through this surface;
- suppose a "material" loop is placed inside a static homogenous magnetic field (the loop is not just imaginary) and suppose we are stretching it or that it rotates or whatever as long as its surface vector is changing. Then there will also be an "induced" voltage in this loop and it will again equal the negative time derivative of the magnetic flux through this surface. Just that this time I would claim that this "induced" voltage is not the voltage (in the sense given above) but rather an "effective" voltage of sorts, in the sense that its effect for almost all intents and purposes is the same as if indeed there was a real voltage present. My claim is a bit presumptuous and I'm not quite sure whether or not it holds but I am quite sure. In any case I would like it for you to tell me how "wrong" I am . Also note that I am ignoring whatever fields the elctrons themselves produce in this case as this would complicate matters greately but I don't think it fundamentally hurts the analysis. Or am I wrong again? ;
- suppose the field changes as well as the surface vector. Again the "effective" voltage (as I would like to put it) is the time derivative of the magentic flux (negative, to be precise).
My teacher disagrees with me and says that the voltage is "real" in all cases and, naturally, I disagree with him. Feel free to do the same, but please argument (I know I haven't been doing much of that but I'm asking you to be better than me ), better still, tell me I'm right.

2. Mar 19, 2006

### Staff: Mentor

...i.e. produced by changing the position, orientation, or shape of the loop...

...i.e. produced by changing the magnetic field inside a fixed loop...

How are the effects of the induced voltage different in the two situations, in your view?

Are you not quite sure, or you quite sure?

Last edited: Mar 19, 2006
3. Mar 19, 2006

### Galileo

I think it's worthwhile to point out that in the case of a changing magnetic field, the curl of E is not zero (Faraday's law) and as such, the concept of voltage as a potential energy per unit charge does not exist. the produced E-field is not conservative. Therefore the term induced emf (electromotive force or electromotance) is used instead of voltage.

In a rotating loop in a magnetic field there will indeed be an emf (a current will run) that is equal to the -change in magnetic flux, but since there is no changing magnetic field, this is not a result of Faraday's law. I's simply the Lorentz-force acting on the charge carriers in the loop.

4. Mar 20, 2006

### vidmar

They are different in the sense that in the first case there is a line integral of the electric field around the loop and in the second (neglecting the fields of the electrons, which again I would say is a reasonable assumption) there is no such voltage (the line integral ...). And yeah, I'm getting surer - at least, that is, I've convinced my teacher, which is quite an acomplishment.

5. Mar 20, 2006

### vidmar

I'd say that one can (even in the case of a non-conservative electric field) always speak consistently about the concept of voltage (just that it is no longer the diffrence of potentials) but rather depends on the curve of integration. The usage of the term emf is applaudable nonetheless (because of what I've written down) - in my language we know not of such distinctions, unfortunately.