Relation between Drift Velocity and Electric Field
Derivation and understanding of the formula relating drift velocity to the applied electric field and relaxation time: vd = (eE/m)τ.
What is Relation between Drift Velocity and Electric Field?
The average velocity attained by charge carriers in a conductor when subjected to an electric field.
Key formula / rule: Drift Velocity
Key points
- Understand the physical mechanism behind drift velocity.
- Derive the relationship between drift velocity, electric field, and relaxation time.
- Explain the factors affecting drift velocity.
- Apply the formula vd = (eE/m)τ in problem-solving.
Common exam trap
Confusing drift velocity with the random thermal velocity of electrons.
Definitions
- Term
Drift Velocity (vd)
- Meaning
The average velocity attained by charge carriers in a conductor when subjected to an electric field.
- Term
Relaxation Time (τ)
- Meaning
The average time interval between two successive collisions of a charge carrier (like an electron) with the ions or atoms in the conductor's lattice.
- Term
Electric Field (E)
- Meaning
A region around a charged particle or object within which a force would be exerted on other charged particles or objects.
Learning objectives
Understand the physical mechanism behind drift velocity.
Derive the relationship between drift velocity, electric field, and relaxation time.
Explain the factors affecting drift velocity.
Apply the formula vd = (eE/m)τ in problem-solving.
Formulae
- Name
Drift Velocity
- Note
Magnitude of drift velocity. 'e' is elementary charge, 'E' is electric field, 'm' is mass of charge carrier, 'τ' is relaxation time.
- Expression
vd = (eE/m)τ
- Name
Force on electron
- Note
Force experienced by an electron of charge -e in an electric field E.
- Expression
F = -eE
- Name
Acceleration of electron
- Note
Acceleration of an electron between collisions.
- Expression
a = F/m = -eE/m
Prerequisites
Basic understanding of electric fields and forces.
Concept of charge and its motion.
Newton's laws of motion (specifically, F=ma).
Common mistakes
Confusing drift velocity with the random thermal velocity of electrons.
Ignoring the role of collisions and relaxation time in limiting the velocity.
Incorrectly assuming drift velocity is very high.
Forgetting the negative sign when considering direction, or not understanding its implication.
Keywords
Drift Velocity
Electric Field
Relaxation Time
Charge Carriers
Conductor
Electron Motion
Collisions
Microscopic Ohm's Law
Practice preview
What is the relationship between drift velocity (v_d) and the applied electric field (E) for a conductor?…
easy
The drift velocity of electrons in a conductor is given by v_d = (eE/m)τ. If the electric field E is doubled, what happens to the drift velocity?…
easy
Which of the following factors does NOT affect the drift velocity of electrons in a conductor, according to the standard formula?…
medium