Why doesn't the electric potential energy of an electron decrease while moving in a circuit away from the negative terminal? This question is concerned with the drop in the potential energy of electrons due to their constantly changing position in a circuit consisting of a wire with no resistance (Ideal).
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1$\begingroup$ It does drop. Why do you think it doesn’t. Please clarify the question $\endgroup$– DaleCommented Jun 21, 2022 at 15:37
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$\begingroup$ @Dale In an ideal conductor? I hope not. $\endgroup$– HTNWCommented Jun 21, 2022 at 15:47
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$\begingroup$ Just to be clear, are you talking about the negative terminal of a battery connected to a wire of zero resistance? $\endgroup$– Bob DCommented Jun 21, 2022 at 15:54
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$\begingroup$ So, let us suppose that there is a closed circuit comprising a battery and a wire of resistance 0 Ω (Ideal wire). We consider the potential difference between any two points on the wire to be 0. Why? because if we consider any arbitrary electron flowing through the circuit away from the negative terminal towards the positive terminal, its position will change constantly and so should its P.E. $\endgroup$– LuciferPCommented Jun 21, 2022 at 15:56
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1 Answer
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You cannot analyze an ideal wire connecting the terminals of an ideal battery, it is an irresistible force meeting an immovable object.
In the case of an ideal wire connected to a real battery, the internal resistance of the battery will drop all of the EMF for the battery. Thus the terminals will be at the same potential and inside the wire the electrons will move without changing potential energy.
In terms of a gravitational analogy, the terminals would be two places at the same elevation connected by a level road. Cars on the road do not change their potential energy.
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$\begingroup$ For completeness: for an ideal battery connected to a real wire, all of the potential drop is across the wire. An educational activity is to look up resistances for real wires (tabulated as milli-ohms per meter, for different wire gauges) and to compare those to the internal resistances of some real batteries. $\endgroup$– rob ♦Commented Jun 21, 2022 at 16:20
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$\begingroup$ Thank you for the answer! but if we consider a circuit comprising an ideal wire and a battery, the potential difference between any two points on the wire is the same and still, we say that an electric current exists between those points and in the entire circuit, why? we know that current can only exist when there is a potential difference between two points. Isn't that a contradiction? $\endgroup$– LuciferPCommented Jun 21, 2022 at 16:25
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$\begingroup$ The gravitational analogy does not seem right to me as an engineering student. In the limit of $R \to 0^+$, the current would momentarily tend to infinity. $\endgroup$– MechanicCommented Jun 21, 2022 at 16:26
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1$\begingroup$ @Dexter said "we know that current can only exist when there is a potential difference between two points." This is not true. I work with superconducting wires all the time and they carry very large currents with no potential difference. Ideal wires do not require a potential difference to have a current. $\endgroup$– DaleCommented Jun 21, 2022 at 16:28
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$\begingroup$ Thank you for the answer!!! but I still have a doubt. In an ideal circuit along with a battery, the electrons moving away from the negative terminal should experience a drop in potential as they are constantly moving away from the -ve terminal towards the +ve terminal, but why isn't that the case? $\endgroup$– LuciferPCommented Jun 21, 2022 at 16:50