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My teacher was explaining emf to me and he was using an example of a simple electrolytic cell. In this example the two electrodes had been placed in the same solution and had been connected by a wire. He said the electron moves from the negative terminal to positive terminal within the wire due to difference in electric potential. But then he went on to say that the electron completes the circuit by moving from positive plate to the negative plate in the solution (the electrolyte) . He explained that the electron is moved towards the negative electrode due to some "non-electrostatic" force which moves the electron opposite to the electric field.what is this "non-electrostatic force"?

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The forces that move an electron from the positive electrode to the negative electrode inside the battery are, of course, electromagnetic in nature, ultimately. One can say that they are chemical forces because of the processes that generate them. However, they are obviously electromagnetic forces in the end--the only other option is gravity which is obviously ridiculous ;)

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