Electric Current and Flow of Charge in a Metallic Conductor

A metallic conductor is held together by a lattice of positive ions, but a large number of its outermost (valence) electrons are not bound to any one ion -- they are free to move throughout the body of the metal, much like the molecules of a gas confined inside a container. These are called free electrons or conduction electrons.

In the absence of any applied electric field, these free electrons move about randomly, colliding again and again with the vibrating ions of the lattice and with one another, changing both speed and direction at every collision. Because this thermal motion is completely random, the number of electrons crossing any imaginary cross-section of the wire in one direction, in a given short time, is (on average) exactly equal to the number crossing in the opposite direction. The net charge transported across the cross-section is therefore zero, and there is no current, even though the electrons themselves are moving extremely fast (typically of order $10^5\ \text{m/s}$).

The moment a battery (or any source of EMF) is connected across the two ends of the conductor, an electric field $E$ is set up inside it, directed from the higher-potential end to the lower-potential end. This field now exerts a steady force $-eE$ on every free electron, superimposed on top of the pre-existing random thermal motion. The result is that, between collisions, each electron picks up a small extra velocity in the direction opposite to $E$ (since the electron's charge is negative), so that the whole free-electron "gas" acquires a slow, net drift in one direction, superimposed on the much faster random thermal jostling. It is this small net drift -- not the fast random thermal motion -- that constitutes the electric current.

Electric current is defined as the rate of flow of electric charge across a given cross-section of a conductor:

or, for a current that may vary with time, $I = dq/dt$. The SI unit of current is the ampere (A), one of the seven SI base units; a current of one ampere corresponds to one coulomb of charge crossing the section every second, $1\ \text{A} = 1\ \text{C/s}$. …