What is Drift Velocity in Physics?

Drift velocity is a key concept in understanding electric current in conductors. It refers to the average velocity attained by charge carriers, such as electrons, under the influence of an external electric field. This microscopic motion forms the foundation of macroscopic current and is essential in various applications in physics and engineering sectors, particularly in JEE Main examinations.

Definition of Drift Velocity

Drift velocity is defined as the average velocity acquired by free charge carriers in a conductor due to an applied electric field. Despite their random thermal motion, the application of an electric field causes a net movement of these particles, leading to a small but measurable drift in a specific direction.

In metallic conductors, electrons act as the main charge carriers. Under thermal equilibrium, their random motion results in zero net displacement. However, the presence of an electric field produces a uniform acceleration in electrons, resulting in a drift superimposed onto this random motion.

Random Motion and Relaxation Time

In the absence of an electric field, electrons inside a metallic conductor move randomly due to thermal energy. These electrons frequently collide with the positive ions of the lattice, resulting in continuous changes in their direction and speed.

The average time interval between two successive collisions of an electron is known as the relaxation time ($\tau$). In typical conductors, the relaxation time is extremely short, of the order of $10^{-14}$ seconds. This parameter plays an important role in determining drift velocity.

Derivation of Drift Velocity Formula

When an electric field $E$ is applied to a conductor, an electron with charge $-e$ experiences a force $F = -eE$. This force produces an acceleration $a = \dfrac{-eE}{m_e}$, where $m_e$ is the mass of the electron.

Between two successive collisions, an electron accelerates for a time $\tau$, acquiring an additional average velocity in the direction opposite to the electric field. The drift velocity ($v_d$) is then given by:

$v_d = a \tau = \dfrac{-eE}{m_e} \tau$

The negative sign indicates that electrons move opposite to the direction of the applied electric field. This relationship directly connects the microscopic motion of electrons to observable electrical phenomena.

Relation Between Drift Velocity and Electric Current

In a conductor of cross-sectional area $A$, let $n$ be the number of free electrons per unit volume (electron density). If each electron moves with drift velocity $v_d$, the total charge crossing any cross-section per second gives the electric current $I$.

The expression for current is:

$I = n e A v_d$

Here, $e$ is the elementary charge. This fundamental equation connects macroscopic current to the microscopic drift of electrons inside the conductor. For more on electric circuits, refer to Understanding Electric Circuits.

Drift Velocity and Current Density

Current density ($J$) is defined as the electric current per unit area of cross section. It is given by:

$J = \dfrac{I}{A} = n e v_d$

Current density is a vector quantity, and its direction is taken as the direction of flow of positive charges. The magnitude of drift velocity in common metals is extremely small, typically of the order of $10^{-4}$ m/s.

Mobility of Charge Carriers

Mobility ($\mu$) defines the ease of movement of charge carriers in a conductor. It is the drift velocity acquired per unit electric field and is given by:

$\mu = \dfrac{v_d}{E}$

Substituting the value of drift velocity, we have:

$\mu = \dfrac{e \tau}{m_e}$

The mobility depends on the charge, mass, and relaxation time of the carrier. Electrons usually have higher mobility than protons because of their much lower mass.

Drift Velocity Formula and Units

The standard drift velocity formula is:

$v_d = \dfrac{-eE \tau}{m_e}$

The SI unit of drift velocity is meters per second (m/s). Drift velocity is generally much lower than the average thermal speed of electrons in a conductor.

Sample Numerical Example: Calculation of Drift Velocity

For copper, the electron density $n$ is about $10^{29}$ m$^{-3}$ and charge $e = 1.6 \times 10^{-19}$ C. Given a current density $J = 1.55 \times 10^6$ A/m$^2$:

Drift velocity, $v_d = \dfrac{J}{n e}$

$v_d = \dfrac{1.55 \times 10^6}{10^{29} \times 1.6 \times 10^{-19}} = 9.7 \times 10^{-5}$ m/s

This very small drift velocity shows that although electrons move rapidly due to thermal motion, the average displacement due to the electric field is minimal. For more numerical problems, refer to concepts in Greatest Physics Experiments.

Dependence of Drift Velocity on Wire Properties

For a wire of cross-sectional area $A$ carrying current $I$, changing the diameter or material alters the drift velocity, as electron density $n$ and area $A$ affect the relation $v_d = \dfrac{I}{n e A}$.

• Increasing area decreases drift velocity for the same current
• Higher electron density results in lower drift velocity
• Material properties influence relaxation time and mobility

Further insight on current and voltage characteristics is available at Difference Between Current and Voltage.

Applications and Importance of Drift Velocity

Drift velocity allows a clear understanding of microscopic charge motion that leads to observable electric current. It forms the basis for Ohm's law, design of electrical conductors, and performance analysis of semiconductor devices.

• Fundamental in Ohm's law derivation
• Crucial for electric circuit analysis
• Affects conductivity and current-carrying capacity

To explore advanced topics like electromagnetic induction, refer to Electromagnetic Induction and AC Revision Notes.

Drift Velocity: Summary Table

A comprehensive understanding of drift velocity is vital for JEE preparations and for the analysis of various electrical devices and phenomena. For information on current measuring instruments, consider Difference Between Ammeter and Galvanometer.

The study of drift velocity bridges the microscopic behaviors of electrons with the macroscopic effects of electric currents observed in daily technology and experimental circuits. For further exploration of circuit-level concepts, refer to Circuits and Networks Overview.