John Denker has pointed out that voltage is not necessarily potential difference, and he has also pointed out that emf is an old term that we should perhaps get rid of.
It seems to me a discussion about this might be beneficial separate from the induced-voltage/induced-current thread that has been taking place.
What is voltage? Is it "what one measures with a voltmeter?" If so, what kind of voltmeter? The old analog meters were actually ammeters with a series resistor. What is that really measuring? Is this different from a vacuum-tube voltmeter? Is this different from a modern voltmeter with FET transistors? How do all of these compare to the old potentiometer measurement with respect to a standard cell?
What is voltage? Is it the "change in electric potential energy per unit charge between two points," or once a reference point is defined, "the electric potential energy per unit charge?" If so, is it then the same thing as the electric potential difference. It seems it would be if dV is defined as dU/q. But it might not be the same as electric potential difference if dV is defined as Edl.
In the latter case, is John correct that voltages are not same as potential differences when the source of the voltage is magnetic rather than electrostatic? (Am I interpreting you correctly, John?)
This reminds me somewhat of the difference between an x-ray and a gamma-ray. How are they defined? Well, an x-ray comes from electronic transitions, and a gamma-ray comes from nuclear transitions. That's the only difference. What, then, do we call it when we measure a high-energy photon after it is away from the atom that generated it? Can we tell whether it is an x-ray or gamma-ray if we don't know whether it came from the nucleus or the electron cloud? Is it okay to call it an x-ray? Is it okay to call it a gamma-ray? Or must we call it something else (like high-energy photon) because we don't know its source?
Is there an analogy between this and voltage versus electric potential? If there is a voltage measured between two wires, but we don't know whether there is a battery, or a charged capacitor, or a generator at the other end of those wires, does that mean we can't call it a potential difference?
The Hyperphysics site defines emf as the voltage that is produced by an electrochemical cell, or by a dissimilar junction, or via Faraday's Law. It this still a useful distinction to differentiate these from voltages caused by electrostatic fields. Also note that the Hyperphysics site defines voltage as "electric potential energy per unit charge."
Michael D. Edmiston, Ph.D.
Professor of Chemistry and Physics
Bluffton University
Bluffton, OH 45817
(419)-358-3270
edmiston@bluffton.edu