what accelerates the electron in the thin part of a current-carrying wire?

Consider a thick wire that narrows for some part of its length, connected to the terminals of a battery, hence carrying some current.

Presumably the electrons have to speed up as the wire gets thinner - if the current is constant everywhere, then if the wire cross-section is less, they have to go through faster in order for the same number of electrons to pass any point in a given time.

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askIITians faculty

mukesh sharma

The speed (drift) of the electrons has nothing to do with the area.