Magnetic induction, Faraday's law and the likes

AI Thread Summary
The discussion centers on the nuances of electromagnetic induction, particularly Faraday's law, and the concept of induced voltage. It highlights the distinction between induced voltage in a static magnetic field versus a changing magnetic field, with the latter yielding an electromotive force (emf) rather than traditional voltage due to the non-conservative nature of the electric field. Participants debate whether the induced voltage in a moving loop should be considered "real" or merely "effective," with one claiming that its effects are similar to real voltage. The conversation also touches on the implications of the curl of the electric field in these scenarios, emphasizing the importance of understanding the context of induced emf. Overall, the thread explores the complexities of voltage and emf in electromagnetic induction.
vidmar
Messages
11
Reaction score
0
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 :rolleyes: . 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? :smile: ;
- 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 o:) ), better still, tell me I'm right.
Thanks for your answers.
 
Physics news on Phys.org
vidmar said:
I would claim that this "induced" voltage

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

is not the voltage (in the sense given above)

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

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.

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

My claim is a bit presumptuous and I'm not quite sure whether or not it holds but I am quite sure.

Are you not quite sure, or you quite sure? :confused:
 
Last edited:
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.
 
jtbell said:
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? :confused:

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.
 
Galileo said:
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.

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.
 
This is from Griffiths' Electrodynamics, 3rd edition, page 352. I am trying to calculate the divergence of the Maxwell stress tensor. The tensor is given as ##T_{ij} =\epsilon_0 (E_iE_j-\frac 1 2 \delta_{ij} E^2)+\frac 1 {\mu_0}(B_iB_j-\frac 1 2 \delta_{ij} B^2)##. To make things easier, I just want to focus on the part with the electrical field, i.e. I want to find the divergence of ##E_{ij}=E_iE_j-\frac 1 2 \delta_{ij}E^2##. In matrix form, this tensor should look like this...
Thread 'Applying the Gauss (1835) formula for force between 2 parallel DC currents'
Please can anyone either:- (1) point me to a derivation of the perpendicular force (Fy) between two very long parallel wires carrying steady currents utilising the formula of Gauss for the force F along the line r between 2 charges? Or alternatively (2) point out where I have gone wrong in my method? I am having problems with calculating the direction and magnitude of the force as expected from modern (Biot-Savart-Maxwell-Lorentz) formula. Here is my method and results so far:- This...
Back
Top