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.
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Sarthak Rout
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The scenario you've described is clear enough, but what exactly are you asking? How to find the surface charge on a current carrying wire? Something else? – Kyle Oman Jun 04 '18 at 07:58
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Yes, I would like to know its distribution. I am even confused as to how field lines are starting and ending on the same surface. – Sarthak Rout Jun 04 '18 at 07:59
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@Sarthak Rout Why do you think that field lines start and end on the same surface ? – Abhinav Dhawan Jun 04 '18 at 08:48
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I am taking a path, a curved one which starts on point A on the wire and ends on another point B in the wire. From A, I leave the surface, kinda fly above it and then land on point A. So, the surface, (can assume cylindrical), is same. I will be adding a pic. – Sarthak Rout Jun 04 '18 at 09:25
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There is an electric field outside a wire. https://physics.stackexchange.com/questions/61884/does-a-current-carrying-wire-produce-electric-field-outside/62166#62166 – Farcher Jun 04 '18 at 09:53
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Possible duplicate of Electric field outside wire with stationary current – sammy gerbil Jun 04 '18 at 10:32
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They were not quite helpful. They give reference to an article which requires paid access. I would like someone to explain it if you have it. – Sarthak Rout Jun 04 '18 at 15:50