Drift Velocity - Meaning, Formula, FAQs

Drift Velocity - Meaning, Formula, FAQs

Team Careers360Updated on 02 Jul 2025, 04:28 PM IST

The free electrons in a conductor are always in a continuous random motion due to the thermal energy of the conductor and the average speed at which free electrons 'drift' in the presence of an electric field is called drift velocity. In this article, we will discuss what is drift velocity, the drift velocity formula, the relation between current density and drift velocity, the relation between drift velocity and electric current, and factors affecting drift velocity. Over the last ten years of the JEE Main exam (from 2013 to 2023), nine questions have been asked on this concept.

This Story also Contains

  1. What is Drift Velocity Class 12?
  2. Drift Velocity Formula Class 12
  3. Relation Between Current Density and Drift Velocity
  4. Relation Between Drift Velocity and Electric Current
  5. Factors Affecting Drift Velocity
  6. Important Terms Related to Drift Velocity
  7. Solved Examples Based on Drift Velocity
Drift Velocity - Meaning, Formula, FAQs
Drift Velocity

What is Drift Velocity Class 12?

Drift velocity definition: Drift velocity is the average velocity that a particle such as an electron attains in a material due to an electric field.

Drift velocity definition in terms of an electron: The drift velocity of an electron in a conductor is the average velocity an electron acquires in the presence of an electric field.

Drift Velocity Formula Class 12

$$V_d=\frac{I}{n A e}$$

where,

  • $V_d$ is the drift velocity of the electrons
  • $I$ is the electric current flowing through the conductor
  • $n$ is the number density of free electrons
  • $A$ is the cross-sectional area of the conductor
  • $e$ is the charge of an electron

Drift velocity in terms of electric field ($E$) and mobility of electrons ($\mu$)

$$
V_d=\mu E
$$

$V_d$ is directly proportional to $E$:

$V_d \propto E$ when the temperature is constant, the greater the electric field, the larger the drift velocity.

Drift velocity varies inversely with the area of the cross-section

Drift velocity

Also, read

SI Unit of Drift Velocity

The SI unit of drift velocity is meters per second ( $\mathrm{m} / \mathrm{s}$ ).

$V_d=\frac{I}{n A e}$

substituting unit of each term

$V_d=\frac{\mathrm{A}}{\left(\mathrm{m}^{-3}\right)\left(\mathrm{m}^2\right) \mathrm{C}}$

$V_d=\frac{\mathrm{A}}{\mathrm{m}^{-1} \cdot \mathrm{C}}$

$V_d=\frac{\mathrm{C} / \mathrm{s}}{\mathrm{m}^{-1} \cdot \mathrm{C}}$

Thus simplifying we get

$$V_d=\frac{\mathrm{m}}{\mathrm{s}}$$

Commonly Asked Questions

Q: What's the relationship between drift velocity and electric field strength?
A:
Drift velocity is directly proportional to electric field strength. A stronger electric field exerts more force on the charge carriers, accelerating them more between collisions and resulting in a higher average velocity in the field direction.
Q: What's the relationship between drift velocity and electron mean free path?
A:
The mean free path, which is the average distance an electron travels between collisions, is directly related to drift velocity. A longer mean free path generally results in higher drift velocity as electrons can accelerate more between collisions.
Q: Why doesn't drift velocity depend on the length of the conductor?
A:
Drift velocity is independent of conductor length because it's determined by local conditions like electric field strength and material properties. Changing the length affects the total voltage needed to maintain the same electric field, but not the drift velocity itself.
Q: How does drift velocity affect power transmission in electrical grids?
A:
Understanding drift velocity is important in power transmission as it relates to current density and power losses. Lower drift velocities for a given current can be achieved with larger conductor cross-sections, reducing resistive losses in long-distance transmission.
Q: How does the relaxation time of electrons affect drift velocity?
A:
The relaxation time, which is the average time between electron collisions, directly affects drift velocity. A longer relaxation time allows electrons to accelerate more between collisions, resulting in a higher drift velocity.

Relation Between Current Density and Drift Velocity

The drift velocity is directly proportional to the current density.

$$
J=n e V_d
$$

where,

$J$ is the Current Density
$n$ is the number density of electrons in a conductor
$e:$ is the charge of an electron
$V_d$ is the drift velocity

Relation Between Drift Velocity and Electric Current

The drift velocity is directly proportional to the electric current.

$$
I=n A e v_d
$$

hence,

$$
I \propto v_d
$$

Factors Affecting Drift Velocity

  1. Electric field
  2. Charge of the electron
  3. The number density of electrons
  4. Temperature
  5. Mobility of electron
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Commonly Asked Questions

Q: Why is drift velocity typically much slower than the actual speed of electrons?
A:
Drift velocity is slow because electrons frequently collide with atoms in the conductor, changing direction randomly. The net movement in one direction is small compared to their total path length, resulting in a low average velocity in the direction of current flow.
Q: Can drift velocity be zero when electrons are moving?
A:
Yes, drift velocity can be zero even when electrons are moving. This occurs when there's no net electric field applied, causing electrons to move randomly with no preferred direction, resulting in zero average velocity.
Q: How does temperature affect drift velocity?
A:
Increasing temperature generally decreases drift velocity. Higher temperatures cause more frequent collisions between electrons and atoms, increasing resistance and reducing the net movement of charge carriers in the direction of the electric field.
Q: Why doesn't increasing voltage indefinitely increase drift velocity?
A:
Increasing voltage does increase drift velocity initially, but it doesn't continue indefinitely. At very high voltages, other factors like electron-electron interactions and relativistic effects come into play, limiting further increases in drift velocity.
Q: What's the relationship between drift velocity and conductor cross-sectional area?
A:
Drift velocity is inversely proportional to the cross-sectional area of the conductor. For a given current, a larger cross-sectional area means more electrons can flow, resulting in a lower drift velocity for each electron.

Important Terms Related to Drift Velocity

  • Relaxation Time (τ):

The time interval between two successive collisions of electrons with the Positive ions.

  • Mean Free Path:

The path between two consecutive collisions is called the free path. The average length of these free paths is called the “Mean Free Path”.

  • Mobility Of An Electron:

It is the drift velocity of an electron per unit electric field. It indicates how easily an electron can pass through the material (conductor or semiconductor) in the presence of an electric field.

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

Recommended Topic Video

Solved Examples Based on Drift Velocity

Example 1: Drift speed of electrons, when 1.5 A of current flows in a copper wire of cross-section is v . If the electron density in copper is $9 \times 1028 / \mathrm{m} 3$ the value of $v$ in $\mathrm{mm} / \mathrm{s}$ is close to (Take charge of an electron to be $=1.6 \times 10-19 \mathrm{C}$ )

1) 0.02

2) 3

3) 2

4) 0.2

Solution:

$\begin{gathered}I=n e A V_d \\ V_d=\frac{I}{n e A}=\frac{9 \times 10^{28} \times 1.6 \times 10^{-19} \times 5 \times 10^{-6}}{1}=0.02 \times 10^{-3} \mathrm{~m} / \mathrm{s}=0.02 \mathrm{~mm} / \mathrm{sec}\end{gathered}$

Hence, the answer is the option (1).

Example 2: A current of 10 A exists in a wire of a cross-sectional area of 5 mm 2 with a drift velocity of $2 \times 10-3 \mathrm{~ms}-1$. The number of free electrons in each cubic meter of the wire is:

1) 1×1023
2) 625×1025
3) 2×1025
4) 2×106

Solution:

\begin{aligned}
&i=10 \mathrm{~A}, A=5 \mathrm{~mm}^2=5 \times 10^{-6} \mathrm{~m}^2 \text { and } v_d=2 \times 10^{-3} \mathrm{~m} / \mathrm{s}\\
&\text { We know, }\\
&\begin{gathered}
i=n e A v_d \\
10=n \times 1.6 \times 10^{-19} \times 5 \times 10^{-6} \times 2 \times 10^{-3} \Rightarrow n=0.625 \times 10^{28}=625 \times 10^{25}
\end{gathered}
\end{aligned}

Hence, the answer is the Option(2).

Example 3: When a 5 V potential difference is applied across a wire of length 0.1 m, the drift speed of electrons is $2.5 \times 10^{-4} \mathrm{~ms}^{-1}$. If the electron density in the wire is $8 \times 10^{28} \mathrm{~m}^{-3}$, the resistivity of the material is close to:

1) $1.6 \times 10-8 \Omega \mathrm{~m}$
2) $1.6 \times 10-7 \Omega \mathrm{~m}$
3) $1.6 \times 10-6 \Omega \mathrm{~m}$
4) $1.6 \times 10-5 \Omega \mathrm{~m}$

Solution:

\begin{aligned}
& I=A n e v_{-} d \\
& \Rightarrow V=R A n e v_{-} d \\
& \Rightarrow V(\rho I / A)=A n e v_{-} d \\
& \Rightarrow V A / \rho I=A n e v_{-} d \\
& \Rightarrow \rho=V / I^*\left(1 / n v_{-} d\right) \\
& \Rightarrow \rho=V I /\left(n e v_{-} d\right) \\
& =50.1 \times\left(8 \times 10^{\wedge} 28\right) \times\left(1.6 \times 10^{\wedge}(-19)\right) \times\left(2.5 \times 10^{\wedge}(-4)\right) \\
& \Rightarrow \rho=1.5625 \times 10^{\wedge}(-5) \Omega \mathrm{m} \approx 1.6 \times 10^{\wedge}(-5) \Omega \mathrm{m}
\end{aligned}

Hence, the answer is the option (4).

Example 4: An electron moving in a zigzag path travels a displaces by 0.2 mm in 10 seconds. Its drift speed is (in $\mathrm{m} / \mathrm{sec}$ )
1) $2 \times 10^{-5}$
2) $10^{-5}$
3) $2 \times 10^{-4}$
4) $10^{-4}$

Solution:

Drift velocity

Drift velocity is the average velocity that a particle such as an electron attains in a material due to an electric field.

wherein

drift velocity

Drift Velocity = Displacement/time

Displacement $=.2 \mathrm{~mm}=2 \times 10^{-4} \mathrm{~m}$

Time = 10 sec

Drift Velocity $V_d=2 \times 10^{-5} \mathrm{~m} / \mathrm{sec}$

Hence, the answer is option (1).

Example 5: Which of the following is correct regarding relaxation time?

1) Relaxation time increases with increase in temperature

2) Relaxation time decreases with increase in temperature

3) A decrease in relaxation time causes a decrease in resistivity

4) Conductivity is independent of Relaxation time

Solution:

Relaxation time ($\tau$)⟶ The time interval between two successive collisions of electrons with the ions/ atoms.

As with an increase in temperature drift velocity increases which will lead to an increase in the rate of collision and hence relaxation time decreases.

Hence, the answer is the option (2).

Frequently Asked Questions (FAQs)

Q: Can drift velocity be used to explain the difference between conductors and insulators?
A:
Yes, the concept of drift velocity helps explain the difference between conductors and insulators. In conductors, electrons can achieve significant drift velocities under an applied electric field. In insulators, the drift velocity is negligible due to the lack of free charge carriers.
Q: How does the concept of drift velocity help in explaining the operation of magnetohydrodynamic generators?
A:
In magnetohydrodynamic generators, the concept of drift velocity is applied to the movement of charged particles in a conductive fluid or plasma. The interaction between the drifting charges and a magnetic field is used to generate electricity, with the drift velocity determining the current density and power output.
Q: What's the significance of drift velocity in understanding electrical noise in conductors?
A:
Drift velocity contributes to our understanding of electrical noise. Fluctuations in drift velocity due to random thermal motion and collisions give rise to thermal noise (Johnson-Nyquist noise) in conductors, which sets fundamental limits on signal detection in electronic systems.
Q: How does drift velocity affect the performance of field-effect transistors (FETs)?
A:
In FETs, drift velocity is crucial for device performance. It affects the transit time of carriers through the channel, influencing the maximum operating frequency and switching speed of the transistor. Velocity saturation at high fields is a key factor in FET design.
Q: Can the concept of drift velocity be applied to superconducting quantum interference devices (SQUIDs)?
A:
While traditional drift velocity doesn't apply in superconductors, the concept is relevant in understanding SQUID operation. The movement of Cooper pairs in response to applied fields and the quantum interference effects are analogous to drift velocity in normal conductors.
Q: How does drift velocity contribute to Joule heating in electrical conductors?
A:
Drift velocity is directly related to Joule heating. As electrons drift through a conductor, they collide with atoms, transferring kinetic energy. This energy transfer manifests as heat, with the power dissipated proportional to the square of the drift velocity.
Q: What's the relationship between drift velocity and the relaxation time approximation in solid-state physics?
A:
The relaxation time approximation assumes that electrons return to equilibrium after a characteristic time following a collision. This approximation is used to derive the expression for drift velocity in terms of the electric field and the average time between collisions.
Q: How does the concept of drift velocity apply to nanoscale electronic devices?
A:
In nanoscale devices, the traditional concept of drift velocity may break down as the device dimensions become comparable to or smaller than the mean free path of electrons. Quantum effects and ballistic transport can become more significant in these cases.
Q: What's the significance of drift velocity in understanding current saturation in semiconductors?
A:
Drift velocity is key to understanding current saturation in semiconductors. As the electric field increases, drift velocity initially increases linearly but eventually saturates due to increased scattering at high fields, leading to a limit on the maximum current density.
Q: How does drift velocity relate to the concept of electron ballistic transport?
A:
Drift velocity and ballistic transport represent different regimes of electron movement. Drift velocity applies when electrons undergo frequent collisions, while ballistic transport occurs when electrons can travel through a material without collisions, typically in very small or highly pure devices.