Drift Velocity- Definition, Formula, Examples

Last Updated on December 15, 2023 by Electricalvolt

The slow movement of electrons in the conductor when an EMF is applied across the conductor is called Drift Velocity. The electrons do not move in a straight line because of the collision of electrons within the conductor. Thus, the collision of electrons with the conductor surface and the collision of electrons with each other distract the path of electrons and reduce the velocity of electrons, and the electrons move randomly in the conductor.

The randomly moving electrons exchange energy during a collision, and the energy moves forward in the opposite direction to the current.

Drift Velocity Definition

The drift velocity is the electrons’ average velocity when subjected to an electric field. Drift velocity means the slow movement of electrons in the opposite direction of the electric field. The movement of electrons happens in the axial direction because of the movement of electrons in a plane. Thus, the electron’s velocity is considered in the axial direction for the calculation of the drift velocity.

The velocity at which free electrons moves slowly and drifted towards the positive supply source of external electric field is called the Drift velocity.

drift-velocity

The SI unit of drift velocity is m/s. It is also measured in m2/(V.s).

Net Velocity of the Electrons:

Every material above absolute zero temperature consists of some free electrons moving at random velocity. However, the net velocity is zero when no external electric field is applied. The electrons move towards the positive potential when the external electric field is applied around a conductor.

The movement of electrons does not happen in a straight line because the electrons collide with the atom and lose their kinetic energy. But the electric field causes electrons to accelerate again, and electrons start moving in the same direction. Thus, the net velocity of electrons will be in the same direction as the electric field.

Drift Velocity Derivation

When a charged particle(electron) is placed in an electric field E, the force(F) experienced by the particle is;

Acceleration of each electron is;

acceleration-formula

From equation(1) & 2, we get;

acceleration-of-charged-particle

The initial thermal velocity of the electron is u1, the final velocity is v1, and the time taken for this collision is t.

collision-of-electrons

The thermal velocity u1 can be expressed as;

thermal-velocity-u1

Similarly, the thermal velocities of other electrons are;

thermal-velocities-of-electron

The average velocity of all the electrons is the drift velocity and can be calculated as follows.

The average velocity is;

average-velocity-of-electron- drift velocity- formula-derivation

Putting the value of thermal velocities from equations 4,5 & 6 in equation 6, we get;

formula-of-vd

Therefore,

drift-velocity- formula-derivation step

The average thermal velocity of electrons inside the conductor is zero when no electric field is applied to the conductor. Therefore, from the equation 10,

average-thermal-velocity-of-electrons

Therefore, equation 10 can be written as;

derivation-of-vd-steps

The equation 11 can be rewritten as;

drift velocity formula derivation
relaxation-time-formula

Therefore,

drift-velocity-and-relaxation-time

Putting the value of a from the equation 3, we get

drift-velocity-formula

Drift Velocity Formula

The formula for Drift Velocity is given as follows

formula-for-drift-velocity

Let us understand some important terms used in the drift current formula.

Average Relaxation Time

The time interval between two successive collisions of electrons in a conductor when an electric field is applied to it. It is denoted by τ(tau).

formula1-for-relaxatio- time

We can express the average relaxation time by the following formula.

formula2-for-relaxation-time

Mobility (μ)

The mobility of electrons depends on the applied electric field to a conductor. The mobility shows how quickly a charged particle can move through a conductor. The electron mobility is the ratio of the drift velocity of an electron to its applied electric field.

mobility-formula

Putting the value of Vd, we get;

formula-for-charged-particle's-mobility

Solved Problems on Drift Velocity

Problem 1: When a potential difference V is applied across a conductor at a temperature T, calculate the drift velocity of electrons.

Solution:

solved-problem1-on-drift-velocity

Problem 2: The mobility of electrons in a silver conductor is 6.9973 × 10-3 m2/v/s, and the Electric field along the wire(E) = 120 volts/m; calculate the drift velocity of electrons.

Solution-

solved-problem2-on-drift-velocity
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About Satyadeo Vyas

Satyadeo Vyas, M.Tech,M.B.A. is an electrical engineer and has more than 36 years of industrial experience in the operation, maintenance, and commissioning of electrical and instrumentation projects. He has good knowledge of electrical, electronics, and instrumentation engineering.

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