# Flow of electrons in circuit

In the paint document you will see on the LHS a picture of a circuit diagram then on the RHS you will see a pictorial representation of an electron in the circuit located at an arbitrary point

My question (which is in the paint document): I want to know why the electrons flow in the direction that they do.

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Do not confuse current flow with electron flow. You may want to investigate Benjamin Franklin and his incorrect assumption about current.

I hope this helps!

vanhees71
Gold Member
There is a lot of confusion, because many people do not tell which flow they talk about. A flow is characterized by a current-density vector, and here there are involved at least two different vectors in this question.

The first is the number-density current of electrons in a wire. If the number density of electrons is $n(t,\vec{x})$ and $\vec{v}(t,\vec{x})$ the velocity field of the electrons, then the number-density current is $\vec{J}_n(t,\vec{x})=n(t,\vec{x}) \vec{v}(t,\vec{x})$. Obviously $n(t,\vec{x})>0$ (giving the number of electrons per unit volume). The number-current density gives the number of electrons per unit time running through a surface element with surface-area vector $\mathrm{d} \vec{F}$ as
$$\mathrm{d}N=\mathrm{d} \vec{F} \cdot \vec{J}_n.$$

The electric current-density vector $\vec{j}_{\text{el}}$, however, gives the charge per unit time running through the surface element. Obviously we have $\vec{j}_{\text{el}}=-e \vec{J}_n$, where $-e<0$ is the charge of one electron. This shows that the electric current-density vector points always in the opposite direction of the number-density current of electrons, simply because (by convention!) electrons are negatively charged.

You can indeed find out, whether the charge carriers of a current are positively or negatively charged by using the Hall effect:

http://en.wikipedia.org/wiki/Hall_effect

It turned out that in metals the charge carriers carry negative charge, while in some semiconductors the charge carriers are negatively charged. In the case of metals the charge carriers are (medium modified) electrons and in the case of p-doted semiconductors positively charged quasiparticles, i.e., electron holes in the Fermi sea.