The charges that move in a conductor are called the charge carriers. FIGURE 27.2 reminds you of the microscopic model of a metallic conductor that we introduced in Chapter 22. The outer electrons of metal atoms—the valence electrons—are only weakly bound to the nuclei. When the atoms come together to form a solid, the outer electrons become detached from their parent nuclei to form a fluid-like sea of electrons that can move through the solid. That is, electrons are the charge carriers in metals. Notice that the metal as a whole remains electrically neutral. This is not a perfect model because it overlooks some quantum effects, but it provides a reasonably good description of current in a metal.

FIGURE 27.2 The sea of electrons is a model of electrons in a metal.

The conduction electrons in a metal, like molecules in a gas, undergo random thermal motions, but there is no net motion. We can change that by pushing on the sea of electrons with an electric field, causing the entire sea of electrons to move in one direction like a gas or liquid flowing through a pipe. This net motion, which takes place at what we’ll call the drift speed $v_{\text{d}}$, is superimposed on top of the random thermal motions of the individual electrons. The drift speed is quite small. As we’ll establish later, ${10}^{-4}\text{m}\text{/}\text{s}$ is a fairly typical value for $v_{\text{d}}$.

As FIGURE 27.3 shows, the entire sea of electrons moves from left to right at the drift speed. Suppose an observer could count the electrons as they pass through this cross section of the wire. Let’s define the electron current $i_{\text{e}}$ to be the number of electrons per second that pass through a cross section of a wire or other conductor. The units of electron current are $\text{s}{}^{-1}$. Stated another way, the number $N_{\text{e}}$ of electrons that pass through the cross section during the time interval $\text{Δ}t$ is

FIGURE 27.3 The electron current.

Not surprisingly, the electron current depends on the electrons’ drift speed. To see how, FIGURE 27.4 shows the sea of electrons moving through a wire at the drift speed $v_{\text{d}}$. The electrons passing through a particular cross section of the wire during the interval $\text{Δ}t$ are shaded. How many of them are there?

FIGURE 27.4 The sea of electrons moves to the right with drift speed $v_{\text{d}}$.

The electrons travel distance $\text{Δ}x=v_{\text{d}}\text{Δ}t$ to the right during the interval $\text{Δ}t$, forming a cylinder of charge with volume $V=A\text{Δ}x$. If the number density of conduction electrons is $n_{\text{e}}$ electrons per cubic meter, then the total number of electrons in the cylinder is

Comparing Equations 27.1 and 27.2, you can see that the electron current in the wire is

You can increase the electron current—the number of electrons per second moving through the wire—by making them move faster, by having more of them per cubic meter, or by increasing the size of the pipe they’re flowing through. That all makes sense.

Depending on the element, each atom contributes one or more valence electrons to the sea of electrons. Thus the number of conduction electrons per cubic meter is an integer multiple of the number of atoms per cubic meter, a quantity that can be determined from the metal’s mass density. TABLE 27.1 gives values of the conduction-electron density $n_{\text{e}}$ for several metals.