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To be more simple, If current $i$ is flowing through a long cylindrical wire does the current density of region $A$ and $B$ same? ...

  • @joseph h I have already made a comparison of the two areas in cylindrical wire, no the areas are different... –  Aug 02 '21 at 06:05
  • So if the current flows uniformly through the wire, what does that tell you about current density through any two areas? – joseph h Aug 02 '21 at 06:50
  • @joseph h Well according to other answers the current density will be same for $A$ and $B$... –  Aug 02 '21 at 06:58
  • Yes. That is correct. If the current is uniform across the wire, then the current density will be the same for any two areas, since j=current/unit area. – joseph h Aug 02 '21 at 07:11

2 Answers2

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It depends on the distribution of current within the wire. This post (Does electricity flow on the surface of a wire or in the interior?) suggests that, for DC current, there will be no (or really very little) difference in current density between the two regions. For AC current, this will not be the case and the current density will be biased towards the surface regions of the wire.

gigo318
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  • It's DC current and all the cases are taken to be ideal –  Aug 02 '21 at 06:05
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    In that case, the current density will be the same. Another way to think about the problem is for an object of uniform mass, the mass density is the same everywhere in the object and does not depend on the size of the volume being considered. The same argument holds for current density and area. When there is a non-uniform distribution of mass/current, you will need to average over the volume/area under consideration. – gigo318 Aug 02 '21 at 06:15
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The answer goes as follows:

let A be the area of cross section of the cylindrical conductor we have considered then the current density is defined as the current flowing per unit area perpendicular to the direction of the flow.

From the above definition you can tell that the total current passing through area is equal to integral of dot product of current density j and area vector dA. Since violet part has more area of cross section, it sustain greater current density than the green part. Hence current is more in violet part.