I encountered a interesting problem. It first invokes the fact that between two points, potential difference is independent of the path between them. Then, it asks you to apply it for a wire carrying constant current I. Path 1: Along the wire. Path 2: Going in a curved path outside the wire. The thing is, a non zero field is needed outside the wire to evaluate (E . dr). It hints of a surface charge density on the wire. But, I am not able to correlate it with our day to day observation or find its distribution mathematically.
closed as unclear what you're asking by Kyle Oman, sammy gerbil, Prahar, ACuriousMind♦ Jun 4 '18 at 17:06
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