# Potential difference across a wire along all paths [closed]

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.

• 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 4 '18 at 7:58
• 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 4 '18 at 7:59
• @Sarthak Rout Why do you think that field lines start and end on the same surface ? – Abhinav Dhawan Jun 4 '18 at 8:48
• 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 4 '18 at 9:25
• There is an electric field outside a wire. physics.stackexchange.com/questions/61884/… – Farcher Jun 4 '18 at 9:53