# Loopless voltage measurement

I think we are all very well familiarized with the classical voltmeter. Classical voltmeter has two conducting wires that bring two potentials into the box. In the box we have well controlled conditions, in which potential difference (voltage) starts current, and current through the galvanometer deflects the pointer. Anyways, conducting wires are absolutely necessary by this method in order to bring potentials to the box.

However, a person posted the question, where it was necessary to measure voltage on the ends of the bar in the magnetic field. Of course, as soon as you do that with classical voltmeter, you create a loop and loop can generate additional voltage you simply do not want. So my half-way question is: Is it possible to make a loopless voltage measurement?

Of course, in principle I could imagine such a measurement: I would make an electric field probe and put it into the bar, measuring electric field along the bar. After I've obtained electric field in the every point of the bar, I could calculate voltage by integrating electric field between bar's ends. However, this seems to be very difficult measurement and conditions are not really controlled.

My final question is: Is there any other loopless conventional method of measurement available?

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You can always guide an electron along the path and extract energy from it. Though that is similar to the "field probe" thingy. –  Manishearth Apr 16 '12 at 11:27
Yes but can you define potential? Potential is defined only for conservative electrical fields! I think this is the idea behind Dmytry's answer –  Pygmalion Apr 16 '12 at 12:07
Emf, not potential. You cannot define absolute potential. You can define the change in energy when traversing a path, this is $\int \bf E\cdot\rm dl$ –  Manishearth Apr 16 '12 at 12:28
change in energy when traversing a path ... divided by charge. Good point. I shall leave this question open for some more time. –  Pygmalion Apr 16 '12 at 12:34
@Pygmalion You may find an answer of mine interesting: physics.stackexchange.com/a/62444/16689. In short, it explains why you will not measure a voltage in loopless circuit. –  FraSchelle Apr 27 '13 at 9:00

## 1 Answer

There is no 'potential' to measure when you have varying magnetic field, as the electric field has non-zero curl then, and does not behave as gradient of any potential. So there is no electric potential kind of 'voltage'. There is only the electromotive force kind of 'voltage', which is defined on a loop.

edit: To address the question for measuring integral electric field along the wire. It seems to me that if you use coaxial cable for the voltmeter leads, you will be able to measure the charge that flows into the outer sheath of the coaxial cable, from which you could calculate the integral of electric field along the path of the voltmeter lead. Then you could subtract this from full integral along the loop which the voltmeter will measure. Not entirely sure this can work though. Never heard of a device like this.

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I think you have a valid point +1, but it remains to be answered if it is possible to measure what is analogous to potential, i.e. change in energy when traversing a path diveded by charge, this is $\int \vec{E} \textrm{d}\vec{s}$. If there won't be any better answers in one week, you have my accepted answer vote. –  Pygmalion Apr 16 '12 at 12:31
Ahh, I see. Hmm. edit: whoops accidentally sent by pressing enter. I'll edit answer, i got an idea. –  Dmytry Apr 17 '12 at 16:59