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I came across a question about charge accumulation. It states that if a steady current flows in a wire composed of a copper and iron wire of same area (see fig), will the charge accumulate on the junction or not?

Question

My Approach: If I consider a battery is connected to the wire (driving the current in it), then it would be taking electrons from iron side and supplying to the copper. It would make the iron end +ve and copper end -ve. Approach - 1 This drives electrons from junction to the end of iron wire making the iron sided junction +ve and copper sided junction -ve, overall developing a n electric field, which further drives the current. Approach - 2

So, according to me, electrons don't accumulate in the wire, but actually get's carried away by the battery (making wire +) and simultaneously supplied by the battery (making wire -ve) which makes the current to flow.

Otherwise, how can current flow in it??

Question: My final question is, am I right or not? Please explain this concept with a great detail to me.

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If the two halves of the wire were made of the same metal and were making a good contact, there would not be any accumulation of charges at the junction.

But, since the metals are different, we have to consider what happens with an electron, when it crosses the junction.

Simplistically, due to the difference of work function values between copper and iron, some work - roughly, equal to the difference between the two work functions - has to be performed in order to move an electron from copper to iron.

Assuming the work function of copper is $4.7eV$ and the work function of iron is $4.5eV$, the required work would be on the order of $0.2eV$.

To perform this work, some electric field has to be applied across the junction and, therefore some accumulation of opposite charges is required to maintain that field.

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  • $\begingroup$ What about the case when wire is of same material? Is my assumption wrong that battery takes and supplies charge simultaneously so, it will become positively and negatively charged? $\endgroup$ – Yash Mittal Nov 5 '18 at 16:17
  • $\begingroup$ @YashMittal When the wire is the same, the voltage and charge will be distributed evenly across the whole length of the wire. Typically, though, battery is not shorted by a wire, since that would produce very high current, so some resistor or other current limiting element is present, in which case only a small voltage drops across the wire and charge distribution along the length of the wire is insignificant. $\endgroup$ – V.F. Nov 5 '18 at 16:32
  • $\begingroup$ So, if there is no charge distribution on wire, how charges flow without electric field? They need some force. $\endgroup$ – Yash Mittal Nov 5 '18 at 16:34
  • $\begingroup$ @YashMittal Quoting myself: "...charge distribution along the length of the wire is insignificant", which is not the same as no charge distribution, which would be the case if the resistance of the wire was zero. $\endgroup$ – V.F. Nov 5 '18 at 17:36

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