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Most physics textbooks and even questions in stack exchange answer the question why there exists a charge buildup in the bends of a current carrying conductor.

But what I am unable to understand is:

  1. why a surface charge gets developed in the straight region of a current carrying conductor?

  2. why there is a gradient of the surface charge density along the length of the wire?

DanielSank
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Danny Paul
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  • Well, there is no gradient along the length of the wire if its the hypothetical infinite example. It will exist for other circumstances, but all of the specifics depend on the situation you're interested in. – Alan Rominger Aug 04 '15 at 15:10
  • How can we say that there exist a surface charge gradient for the finite length? – Danny Paul Aug 04 '15 at 15:12
  • what intrigues me even more is why the surface charge in the straight regions? – Danny Paul Aug 04 '15 at 15:25

1 Answers1

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In order to have an electric field that follows the path of the wire whether it is straight or curving you must take into consideration the electric fields created by the charge build up at the ends of the battery. Then in order to have a straight electric field in the straight bits of the wire there has to be surface charge there that compensates for the fields created by the battery surface charge.

Also consider that in the steady state the current everywhere in the circuit is the same. This means that the large electric field near the ends of the battery must be somewhat counter acted by nearby surface charge whether the wire is straight or not. Otherwise too much charge would flow near the battery ends and we know this isn't true in the steady state.

Alex
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