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What is the potential in the circuit?
"I think that when electrons move directionally in an electric field, the electric field force will do work." This statement is incorrect. Counterexample: The direction of electron movement is perpendicular to the direction of the electric field lines, and the electric field force does no work.
The distribution of electric field lines in conductors is extremely complex. The conductor is composed of positive ions and free electrons. The electric field at any point in the conductor is (1) the electric field generated by the external power supply there (2) the electric field generated by all positive metal ions (3) the electric field generated by all free electrons, The vector sum of the three. Therefore, it is entirely possible for electrons to move in a conductor and the electric field force to do no work. This is different from the movement of electrons between the two plates of a capacitor in a vacuum. The average electric field line distribution between the two plates of the capacitor is much simpler.
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