If area is not uniform then how can current be constant? What happens to current density, electric field, drift speed? Are they constant?
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asked Jan 13, 2016 at 19:56
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$\begingroup$ How would the current not be constant? Where would it disappear to and reappear from? $\endgroup$– Jon CusterCommented Jan 13, 2016 at 20:22
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$\begingroup$ Ummmm yeah and what about the other things $\endgroup$– rishabh guptaCommented Jan 13, 2016 at 20:54
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$\begingroup$ Well, what about them? Assuming the total current remains constant, what happens? $\endgroup$– Jon CusterCommented Jan 13, 2016 at 21:02
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$\begingroup$ Electric field and drift velocity should be same, isn't it? $\endgroup$– rishabh guptaCommented Jan 14, 2016 at 10:58
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1 Answer
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If the current is steady, then the integral of current density on each cross section is constant. Therefore current density (and, through Ohm's law, electric field) will vary with cross section.
For an arbitrary shape you have to solve Laplace's equation to get the potential inside the conductor, setting mixed boundary conditions: fix potential on both ends, and fix a zero normal derivative on the side surface (so no current escapes). Taking the gradient of this potential gives you electric field and, through Ohm's law, current density.
