Physics · Ch 3 — Current Electricity

Electric Currents in Conductors

3.3

Electric Currents in Conductors

Why Do Conductors Conduct?

In a conductor, some electrons are free — not bound to any particular nucleus. When no electric field is present, these electrons move randomly due to thermal energy. They collide with fixed positive ions, but after each collision, their direction is completely random. At any instant, as many electrons move in one direction as in the opposite direction. Hence, the net current is zero.

What Happens When an Electric Field Is Applied?

If an electric field $\vec{E}$ is applied across a conductor, each free electron experiences a force:

\vec{F} = -e \vec{E}

This force accelerates the electron in the direction opposite to $\vec{E}$ (since the electron's charge is negative). The electron now has a drift superimposed on its random thermal motion. This net motion of charge constitutes an electric current.

The Need for a Steady Electric Field

Consider a cylindrical conductor of radius $R$ . If you place a positive charge $+Q$ on one end and $-Q$ on the other, an electric field is set up from $+Q$ to $-Q$ . Electrons drift toward $+Q$ and neutralise the charges. As soon as the charges are neutralised, the field vanishes and the current stops. So this gives only a short-lived current.

To get a continuous (steady) current, you need a mechanism that maintains a constant electric field inside the conductor — for example, a battery or cell. It supplies fresh charges to the ends, replacing those neutralised by the moving electrons. Under a steady field, the current is also steady.

Key Points About Current in Solid Conductors …

Figure 3.1Charges +Q and –Q put at the ends of a metallic cylinder. The electrons will drift because of the electric field created to neutralise the charges. The current thus will stop after a while unless the charges +Q and –Q are continuously replenished.

Fig. 3.1 — Charges +Q and –Q put at the ends of a metallic cylinder. The electrons will drift because of the electric field created to neutralise the charges. The current thus will stop after a while unless the charges +Q and –Q are continuously replenished.

Drawn by us to help you understand the concept clearly, and verified to make sure it's accurate. For exams, practice from your NCERT textbook's own diagram.

What the Figure Shows

The figure is a schematic of a cylindrical metal conductor drawn in perspective. The left end of the cylinder is marked with a cluster of + signs and labelled +Q; the right end has – signs and is labelled –Q. Inside the cylinder, a bold horizontal arrow points from the positive end toward the negative end, labelled E. There are no axes or scales — the diagram is purely conceptual.

Physical Idea

The figure illustrates the origin of a transient current in a conductor. When opposite charges are placed at the two ends of a metal rod, an internal electric field $\vec{E}$ is set up, directed from the positive to the negative end. This field exerts a force on the free electrons inside the metal, causing them to drift toward the positive end. As electrons move, they neutralise the excess charges at the ends. Once the charges are fully neutralised, the electric field vanishes and the current stops. The diagram shows the initial condition just after the charges are applied, before any neutralisation occurs.

Key Formula Developed from This Figure

The textbook uses this scenario to introduce the drift velocity of electrons. Under a steady electric field $E$ , an electron of mass $m$ and charge $e$ experiences a constant acceleration:

a = \frac{eE}{m}

Between collisions with fixed ions, the electron's velocity increases linearly. If the average time between collisions (relaxation time) is $\tau$ , the drift velocity $v_d$ is:

v_d = \frac{eE}{m} \tau

The current density $j$ (current per unit cross-sectional area) is then:

$j = n e v_d = \frac{n e^2 \tau}{m} E$ …

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