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Let's consider a circuit with a ideal source of emf and a resistor. Consider the segment of wire that connects emf with resistor. If we measure potential difference at any point of the wire, this will be zero or near zero. But charge are moving like it there would be voltage equal of emf.

Why there is a contradiction and how to explain it?

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  • $\begingroup$ You say "If we measure potential difference at any point of the wire". Potential difference is measured between two points. Which is the other point? $\endgroup$ – Sofia Mar 5 '15 at 18:36
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Anything (charges or any objects) can move at constant speed in vacuum without requiring any force exerted on it. That's just Newton's first law of motion.

Here, the charge is not in a vacuum but in a wire where you assume that the resistance is negligible. In reality that is impossible in a regular metal wire at normal temperatures : there MUST be a very small electric field to exert a force on the charge and force it down the wire. This electric field corresponds to a very small potential difference.

Now, if you have a much more resistive segment down the road ("the resistor"), you can assume that, in comparison, the resistance of the wire is nearly zero.

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    $\begingroup$ but the user has to understand that potential difference is between two points, and not at a point. $\endgroup$ – Sofia Mar 5 '15 at 19:13
  • $\begingroup$ Agreed. Since I assumed that he was quoting a question from a homework, I assumed that, when saying "a point", he actually meant "two points seperated by an infinitesimal distance". $\endgroup$ – Teacher77 Mar 7 '15 at 1:14

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