Why do electrons flow through wires?

They don’t. At least, not in the way most people imagine electricity.

Conductors are materials that have a high number of electrons and are relatively free to move. These are the “outer shell electrons” of the atoms in which the material is made. They are sometimes referred to as a “sea”, or a pool, of free electrons, but they are not bound to their respective elements. An electrical current does not involve a steady, high-speed flow from one point to the next of electrons in a way similar to water flowing downstream. However, this analogy is often used to explain it.

Instead, imagine the electrons in a wire like a pipe with ball bearings at each end. A new ball bearing can be pushed in at one end and a ball will “immediately” pop out the other. I have transferred energy very quickly, even though not one ball bearing has traveled very fast or very far. This is how electric current works; even though the conductor contains particles (electrons), electrical energy “flows” extremely quickly through it. However, these particles aren’t moving very fast or very far in any particular case.

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