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If electrons move through the wire because of the force applied by the electric field that attracts them from negative terminal to positive terminal and this force is setting them to motion in a direction not opposing to the direction of the force, why don't they gain potential energy as there is work being done on them?

And like this even if they lose the potential energy, they gained from the chemical reactions inside the battery, on a lamp or a resistor they should gain some energy as they move.

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You are partially correct, as Potential due to a positive charge is given by V= $\frac {kq}{r}$. As an electron moves towards a proton it goes from a region of lower potential to higher potential. But I assume that you know $\Delta U$=$\Delta$Vq. Hence Change in Potential energy is equal to Change in potential multiplied by Charge as Change in Potential is positive, also as q is negative Change in Potential Energy is negative and electron loses Potential Energy and gains Kinetic Velocity. Hope you understand. Cheers

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  • $\begingroup$ Unfortunately, I don't know what ∆U= ∆Vq or V= kq/r means. My teacher did the worst thing ever she gave us the magnetism and electricity unit without giving us the general physics unit first which explained force, potential energy, power...etc. I only started searching for them when I found that the electricity rules didn't make sense. Anyway I'll google it ;) $\endgroup$
    – Manar
    Commented Aug 1, 2020 at 13:56
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    $\begingroup$ I suggest you read from Haliday Resnick or University Physics by Sears and Zarnecky $\endgroup$ Commented Aug 1, 2020 at 14:59
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    $\begingroup$ Also to make it simpler all I'm saying is that the original potential energy it had is getting converted into kinetic energy and so potential energy is lost because kinetic is gained $\endgroup$ Commented Aug 1, 2020 at 14:59
  • $\begingroup$ Do you know Ohm's law? $\endgroup$
    – my2cts
    Commented Aug 1, 2020 at 15:48
  • $\begingroup$ But like that every time sb would apply a work on sth and it moved, the potential energy that that thing gained would be lost as kinetic energy.... And yes I know Ohm's law and rules regarding power too (how come my teacher explained them if we weren't introduced to terms like force, work and power first—idk) but unfortunately we're not going to cover the rules Naruto Uchiha wrote above, I checked the syllabus. $\endgroup$
    – Manar
    Commented Aug 1, 2020 at 16:31

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