Difference Between Drift Velocity and Electric Current Explained
Drift velocity is a fundamental concept in electromagnetism and solid-state physics. It describes the average velocity that charged particles, such as electrons, acquire within a conductor under the influence of an external electric field. While these electrons move in random directions due to thermal energy, the presence of an electric field causes a net movement, or “drift,” resulting in electric current.
In the absence of an electric field, electrons move randomly and their average velocity in any direction is zero, leading to no net flow of charge. Once an external field is applied, each electron experiences a force opposite to the direction of the field, with continuous acceleration interrupted by countless collisions with heavier positive ions. This process results in a small, constant net velocity superimposed on the random motion—called the drift velocity.
Definition of Drift Velocity
Drift velocity is the mean velocity attained by the free electrons of a conductor in the direction opposite to the applied electric field. During motion, electrons frequently collide with ions. Between two collisions, an electron gains speed in one direction (opposite to the field), but this gain lasts only until the next collision, when its velocity resets randomly.
The mean time between collisions is called relaxation time, typically of the order of 10-14 seconds for conductors.
Derivation and Formula of Drift Velocity
When a voltage is applied across a conductor, it sets up an electric field inside. Free electrons, due to their negative charge, experience a force opposite to this field. As a result, they start drifting slowly, facing numerous collisions with positive ions. This effective displacement per unit time is the drift velocity.
Let the applied electric field inside the conductor be E. The acceleration ‘a’ of an electron (charge = -e, mass = m) due to this field is:
Due to frequent collisions, the average velocity gained by an electron in the direction of the field during the relaxation time (τ) is:
This value is averaged over all free electrons in the metal.
| Physical Quantity | Symbol | Formula | Units |
|---|---|---|---|
| Drift Velocity | vd | (I) / (n e A) | m/s |
| Current (from drift velocity) | I | n e A vd | A (ampere) |
| Electron Mobility | μ | vd / E | m2 V-1 s-1 |
Relation Between Drift Velocity and Current
Consider a wire of radius r and area of cross-section A, containing free electrons with number density n. The relation between drift velocity and current is:
Where I is the current, e is the electronic charge (1.6 × 10-19 coulombs), n is the free electron density, and vd is the drift velocity.
Mobility of Charge Carriers
Mobility (μ) expresses how easily an electron moves under an electric field. It is defined as the drift velocity per unit electric field:
For a given material at constant temperature, mobility remains constant. Electrons generally have much higher mobility compared to positive charge carriers in conductors.
Key Steps for Solving Drift Velocity Problems
| Step | Action | Tip |
|---|---|---|
| 1 | List all provided values (I, n, e, A) | Ensure consistent SI units throughout |
| 2 | Identify the suitable formula based on what is missing | Use vd = I / (n e A) or I = n e A vd |
| 3 | Substitute values and solve stepwise | Pay attention to powers of ten |
| 4 | Check physical meaning and units of the answer | Final value should reflect net drift (very small!) |
Worked Example
Suppose a copper wire of area 2 × 10-6 m2 carries a current of 3 A, and the number density of free electrons is 8.5 × 1028 m-3.
Insert the known values:
So, the drift velocity is extremely small, showing electrons move slowly despite the instantaneous effect of switching on a current.
Sample Practice Question
If a current I flows through a wire of diameter d and the electron drift velocity is v, how will the drift velocity change if the same current flows through a wire of diameter 2d made of the same material?
Answer: Since I = n e A vd and A ∝ d2, doubling diameter means area increases four times. To maintain same current, drift velocity decreases by a factor of 4.
| Quantity | Expression | Unit |
|---|---|---|
| Drift velocity of electrons | vd = I / (n e A) | m/s |
| Current from drift velocity | I = n e A vd | A |
| Number density (n) | n = ρ NA / M | m-3 |
Quick Revision Points
- Drift velocity is very small compared to random thermal velocity of electrons.
- Current is directly proportional to drift velocity for a given material and area.
- Mobility links drift velocity and electric field; higher mobility means electrons drift faster.
- Larger wire diameter (area) reduces required drift velocity for the same current.
Explore and Learn More
- Access detailed revision notes and stepwise solved problems on Drift Velocity with Vedantu resources.
- Join interactive classes and practice numericals for strong command over current electricity topics.
- Work through application-based questions to master the use of drift velocity in Physics exams.
For further learning and practice, check more topics and resources on Vedantu’s Physics portal.
FAQs on Drift Velocity: Meaning, Formula, Derivation & Application
1. What is drift velocity?
Drift velocity is the average velocity with which free electrons move through a conductor when an electric field is applied.
Key points:
• Drift velocity is usually in the direction opposite to the electric field for electrons.
• It results from the net movement caused by the electric field, despite random thermal motion.
• It is crucial for understanding how electric current flows in metals and conductors.
2. What is the formula for drift velocity?
The drift velocity (vd) formula is:
vd = I / (n e A)
Where:
• I = electric current (A)
• n = number density of electrons (m-3)
• e = charge of an electron (1.6 × 10-19 C)
• A = cross-sectional area (m2)
3. What is the difference between drift velocity and average velocity?
Drift velocity refers to the slow, net motion of electrons along a conductor due to an applied field, while average velocity includes both random thermal motion and drift.
• Drift velocity is much smaller than the random thermal (average) velocity.
• Only drift velocity contributes to current flow.
4. How is drift velocity related to electric current?
Electric current (I) and drift velocity (vd) are directly proportional.
The relationship is:
I = n e A vd
• Increasing drift velocity increases current for a given conductor.
• Number density and area also affect current.
5. What are the SI units of drift velocity?
The SI unit of drift velocity is meter per second (m/s).
• It measures how fast electrons drift in a conductor under an applied field.
6. Why is drift velocity so small even though the electric current is large?
Drift velocity is very small because the number of electrons per unit volume (n) in a conductor is extremely large.
• Large current can flow even with a tiny drift velocity due to the massive number of moving electrons.
• For example, in copper, drift velocity is usually only about 10-4 m/s for common currents.
7. What factors affect drift velocity?
Drift velocity depends on:
• The magnitude of electric current (I)
• Number density of free electrons (n)
• Charge of the electron (e)
• Cross-sectional area of the conductor (A)
• Material properties (like electron mobility)
8. What is mobility and how is it related to drift velocity?
Mobility (μ) is the drift velocity per unit electric field applied to a conductor.
Formula:
μ = vd / E
• Higher mobility means electrons can achieve higher drift velocity for the same electric field.
• It is intrinsic to the material and is higher for conductors like silver and copper.
9. How does temperature affect drift velocity?
As temperature increases, the number of collisions between electrons and ions increases, reducing the average relaxation time and generally decreasing drift velocity for the same electric field.
• Electrical resistance increases with temperature, affecting drift velocity due to more frequent collisions.
10. What is the relationship between drift velocity and current density?
Current density (J) is related to drift velocity as:
J = n e vd
• Current density is the amount of current flowing per unit area.
• Drift velocity directly affects how much current passes through a cross-section.
11. Is drift velocity the same for different metals?
No, drift velocity varies for different metals even if current is the same.
• Number density of free electrons (n) changes with material.
• For the same current, conductors with higher n will have lower drift velocity.
12. Can drift velocity be calculated for holes in a semiconductor?
Yes, drift velocity can be defined for positive charge carriers (holes) in semiconductors.
• The formula structure remains the same, with n replaced by hole density, and e as the elementary charge.
• Both electrons and holes contribute to current in semiconductors.
