electromagnetism - If electromagnetic induction generates a potential difference in a loop, where are the "high" and "low" potentials?

In AP Physics, I learned that when a changing magnetic flux generates an electromotive force around a loop, and emf is measured in volts, where are the "high" and "low" points to measure the potential difference?

Also, how is electromagnetic induction consistent to the conservation of energy?

Answer

A vector field has to have certain properties in order for us to define a scalar potential for it. In particular a vector field $\vec{F}$ must have a vanishing curl: $\nabla \times \vec{F} = 0$ (as well as a couple of other conditions that the electrostatic field also obeys). However, that is exactly the condition that Faraday's law says does not apply in the presence of a time varying magnetic field: $$ \nabla \times \vec{E} = \frac{\partial \vec{B}}{\partial t} \,.$$ So the short version is that you can't define a potential for an induced electric field. Of for the total field composed of electrostatic contributions and magnetodynamic contributions.

However, that does not spell doom for energy conservation, because having a potential is not required for energy to be conserved. Having a potential is required for the energy of a configuration to be independent of how the configuration was achieved. Basically this means that energy conservation is fine, but a important tool has been removed from your problem solving toolkit in these cases. ::sigh::

Cem's answer explains how to understand the behavior of circuits when there are time varying magnetic fields about, but if you have a free movement of charges through space, things get pretty complicated in a hurry.

---

So an interesting question here is, 'So, why do people say it "makes a potential difference in a loop" if there isn't really a potential function?!?'.

That is a very good question and I'm glad you asked it.

I really wish I had a good answer, but I think it is a matter of sloppy language and/or un-rigorous usage. If we restrict ourselves to any non-closed segment of wire, we can blythely ignore the failure to be able to construct a true, global potential function and construct one that will work well enough in the space we are interested in. That is basically what cem suggests, and for a lot of purposes it will work just fine.