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When a conducting wire is connected to a battery, potential difference is set up inside the battery. But, what is the case of a simple conducting wire which has free electrons inside it(without connecting it to a battery)? There are still electrons inside the wire, so do not they repel each other and set up high and low potential without being connected to a battery? But a simple metal wire is not charged(until connected to a battery), so how does that work? How is the electric potential evenly distributed so that there is no overall charge?

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The wire is neutral because there are as many positively charged protons as negatively charged electrons. When connected to a battery, the electromotive force sets up an electric field and the electrons get pushed along. In the wire's rest frame, it is still neutral because the number of charges does not change. The electrons in the metallic wire are not free; they are only delocalized due to the metallic bonds.

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    $\begingroup$ @Shanza to elaborate on why the electrons are not free (which I have had to defend on this site before), is that in physics we use "free" to mean no interactions with anything (i.e. no forces acting on the electron). The electrons here will still interact with atoms in the wire, and they are being pushed by the field from the battery. Typically when first learning about conductors people say they are conductors due to "free electrons", but they really just mean unbound electrons. The word free has a specific meaning in physics. $\endgroup$ – Aaron Stevens Sep 30 '18 at 13:10

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