Drift Velocity — Revision Notes

⚡ 30-Second Revision

Definition — Average velocity of charge carriers due to electric field.
Formula 1 (with E-field) — $v_d = \frac{eE\tau}{m}$ (magnitude for electrons)
Formula 2 (with Current) — $I = nAev_d$
Current Density — $J = nev_d$
Mobility — $\mu = \frac{v_d}{E} = \frac{e\tau}{m}$
Direction — Opposite to $E$ for electrons, opposite to conventional current.
Magnitude — Very small (mm/s), much less than thermal velocity.
Temperature Effect (metals) — $\uparrow T \implies \downarrow \tau \implies \downarrow v_d \implies \uparrow \rho$.

2-Minute Revision

Drift velocity ($v_d$) is the tiny, average directed speed of charge carriers (electrons) in a conductor when an electric field ($E$) is applied. It's superimposed on their much faster, random thermal motion.

The electric field exerts a force, causing electrons to accelerate, but frequent collisions with lattice ions limit this acceleration, resulting in a constant average drift velocity. The magnitude of drift velocity is given by $v_d = \frac{eE\tau}{m}$, where $e$ is electron charge, $\tau$ is relaxation time (average time between collisions), and $m$ is electron mass.

This shows $v_d$ is directly proportional to $E$ and $\tau$. Electric current ($I$) is directly linked to drift velocity by $I = nAev_d$, where $n$ is the number density of free electrons and $A$ is the cross-sectional area.

Electron mobility ($\mu = v_d/E$) measures how easily electrons drift. Remember, drift velocity is opposite to the electric field for electrons and opposite to conventional current. Increasing temperature in metals decreases relaxation time, thus reducing drift velocity and increasing resistance.

5-Minute Revision

Drift velocity ($v_d$) is a fundamental concept explaining how electric current flows at a microscopic level. In a conductor, free electrons are in constant, rapid, random thermal motion. When an external electric field ($E$) is applied, it exerts a force on these electrons, causing them to accelerate.

However, due to frequent collisions with the positive ions of the conductor's lattice, this acceleration is interrupted. The electrons achieve a small, average velocity component in the direction opposite to the electric field (for negative charges), which is the drift velocity.

This $v_d$ is typically very small, on the order of $10^{-4}$ m/s, vastly slower than the electrons' thermal speeds ($10^5-10^6$ m/s) or the speed of the electrical signal (near speed of light).

Key formulas to remember are:

1
Drift velocity in terms of electric field — $v_d = \frac{eE\tau}{m}$, where $e$ is the electron charge, $E$ is the electric field strength, $\tau$ is the relaxation time (average time between collisions), and $m$ is the electron mass. This formula highlights that $v_d \propto E$ and $v_d \propto \tau$.
2
Current in terms of drift velocity — $I = nAev_d$, where $n$ is the number density of free electrons, $A$ is the cross-sectional area of the conductor. This equation is crucial for relating microscopic electron motion to macroscopic current.
3
Current Density — $J = nev_d$. This is the current per unit area.
4
Electron Mobility — $\mu = \frac{v_d}{E} = \frac{e\tau}{m}$. Mobility quantifies how easily electrons move under an electric field.

Example: A wire has $n = 5 \times 10^{28},\text{m}^{-3}$, $A = 2 \times 10^{-6},\text{m}^2$, and carries $I = 1.6,\text{A}$. Find $v_d$. Using $I = nAev_d \Rightarrow v_d = \frac{I}{nAe}$. $v_d = \frac{1.6}{(5 \times 10^{28}) \times (2 \times 10^{-6}) \times (1.6 \times 10^{-19})} = \frac{1.6}{16 \times 10^3} = 0.1 \times 10^{-3} = 1.0 \times 10^{-4},\text{m/s}$.

Important points for NEET:

Drift velocity is opposite to the direction of conventional current.
Increasing temperature in metals decreases $\tau$ (more collisions), which in turn decreases $v_d$ for a given $E$, leading to increased resistance.
Do not confuse drift velocity with the speed of light (signal propagation) or thermal velocity.

Prelims Revision Notes

Drift Velocity (PHY-13-01-02) - NEET Revision Notes

1. Definition & Concept:

Drift Velocity ($v_d$) — The average velocity acquired by free electrons in a conductor under the influence of an external electric field. It's a small, directed velocity superimposed on random thermal motion.
Thermal Velocity — Random, high-speed motion of electrons due to temperature. Average thermal velocity is zero.
Direction — For electrons, $v_d$ is opposite to the electric field ($E$) and opposite to the conventional current direction.
Magnitude — Very small (typically $10^{-4}$ to $10^{-3},\text{m/s}$), much smaller than thermal velocity ($10^5$ to $10^6,\text{m/s}$) and the speed of light (signal propagation).

2. Key Formulas:

Drift Velocity in terms of Electric Field — $v_d = \frac{eE\tau}{m}$

* $e$: magnitude of electron charge ($1.6 \times 10^{-19},\text{C}$) * $E$: electric field strength * $\tau$: relaxation time (average time between collisions) * $m$: mass of electron ($9.1 \times 10^{-31},\text{kg}$)

Current in terms of Drift Velocity — $I = nAev_d$

* $n$: number density of free electrons (electrons per unit volume) * $A$: cross-sectional area of the conductor

Current Density — $J = nev_d$ (vector form $\vec{J} = ne\vec{v_d}$ for positive charge carriers, or $\vec{J} = n(-e)\vec{v_d}$ for electrons)
Electron Mobility — $\mu = \frac{v_d}{E} = \frac{e\tau}{m}$

3. Proportionalities (Crucial for MCQs):

$v_d \propto E$ (for constant $\tau, m$)
$v_d \propto \tau$ (for constant $E, m$)
If $I$ is constant: $v_d \propto \frac{1}{A}$ (since $I = nAev_d$)
If $E$ is constant: $v_d$ is independent of $A$.

4. Effect of Temperature (for Metals):

Increase in temperature ($\uparrow T$) $\implies$ increased lattice vibrations $\implies$ more frequent collisions $\implies$ decrease in relaxation time ($\downarrow \tau$).
Since $v_d \propto \tau$, $\downarrow \tau \implies \downarrow v_d$ for a given $E$.
This decrease in $v_d$ leads to an increase in resistivity ($\uparrow \rho$) and decrease in conductivity ($\downarrow \sigma$).

5. Common Misconceptions to Avoid:

Do not confuse drift velocity with the speed of light (speed of signal propagation).
Do not confuse drift velocity with thermal velocity (magnitudes and directions are vastly different).
Electrons do not continuously accelerate; they achieve an average constant drift velocity due to collisions.
Number density ($n$) affects current for a given $v_d$, but $v_d$ itself (for a given $E$) is independent of $n$.

Vyyuha Quick Recall

To remember the current formula $I = nAev_d$: I Need An Electron Velocity Data. (I = n A e v_d)