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I have learnt that the potential in a point in an electric field is defined as being numerically equal to the work done in bringing a unit positive charge from infinity to the point. However, this is in the case of an electric field. What is the potential in a circuit say, consisting of a battery and simple capacitor, at one of the plates? Is it numerically equal in the work done in moving a unit charge from the 'positive' plate to the positive pole of the battery? (by having to do work in overcoming the attractive forces of the nucleus on the electrons of that plate) But from definitions this charge is a unit positive charge. This is all confusing to me and it would help for simple explanations.

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Usually one doesn't discuss potentials at a plate of the capacitor. One discusses the "potential difference" between the two plates of the capacitor. "Voltage" is always a difference between one point and another.

The voltage on the electricity supply in your house is the difference in potential between the line on the socket and the ground outside your house. What potential any of these things are with relation to a point at infinity is too complex a problem for practical purposes.

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  • $\begingroup$ Actually, I think there is a practical reason to still think about the voltage between a particle and infinity. Because of the dependence on 1/r it will always be zero, which in essence defines a reference or "ground" voltage. $\endgroup$ – Michael Burt Oct 26 '16 at 2:19
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In a circuit, you usually define potential differences with respect to a chosen (arbitrary) electrode. This is often the "mass" electrode which is connected to earth. When you measure potential differences in a circuit, you actually measure differences in electrochemical potential, not the difference in electrical potential. This can be easily recognized when measuring the voltage between two connected wires of different metals, e.g. copper and tin. Already without any applied voltages, there is an electrical potential difference, the contact voltage, which, however, cannot be measured with a voltage meter because both wires have the same electrochemical potential.

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