Right now I'm holding a voltmeter. I measure the voltage between terminals of a AAA battery. It reads 1.47V. Next I measure the voltage between the positive terminal of the battery and my hand (I'm not touching the battery with any part of my body) - 0V. The same goes for my hand and the negative terminal. Now, voltage is the line integral of the electric field and line integrals are path independent in conservative fields, so I expect that $V_{positive-negative} = V_{positive-hand} + V_{hand-negative}$. Yet, 0 + 0 clearly doesn't yield 1.47. Why doesn't the path independence principle hold in this case?
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If you attach a voltmeter between two otherwise isolated things (e.g. a battery and something else such as an isolated metal sphere) then current will begin to flow through the voltmeter from the one initially at higher to the one at lower potential. If the capacitance of the objects is not too large, then it won't take long for this current to change the potential of one or both till they are at equal potential. This accounts for your observations. In this case it is the battery which does not have much capacitance; your body has larger capacitance, and planet Earth a very much larger one. However, you were probably reasonably well isolated from the Earth for your experiment, so you could ignore the latter. The main point is that the battery can quickly be brought to one potential or another when it is contacted with other things; we say it is "floating".
Andrew Steane
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