Drift velocity and carrier mobility Assertion (A): The drift velocity of electrons in a conductor or semiconductor is proportional to the applied electric field E. Reason (R): The ratio of drift velocity to electric field is called the mobility of the charge carrier.

Introduction / Context:
Carrier transport under an applied electric field is a cornerstone of electronic device physics. The concepts of drift velocity and mobility appear in conductivity, Ohm’s law at the microscopic level, and current–voltage characteristics of semiconductors and metals.

Given Data / Assumptions:

• Low-field (ohmic) regime where velocity is proportional to field.
• Scattering time and effective mass define mobility in simple Drude-like models.
• Temperature and impurity concentration influence mobility but not the definition.

Concept / Approach:

In the low-field regime, v_d = μ E, where v_d is drift velocity and μ is mobility. Thus v_d ∝ E, and μ ≡ v_d / E. This linearity breaks down only at very high fields (velocity saturation, hot-carrier effects), but for ordinary operation the proportionality is valid and mobility provides the constant of proportionality.

Step-by-Step Solution:

Verification / Alternative check:

Conductivity σ = q n μ in semiconductors (or σ = q p μ_p for holes) connects mobility to measurable current density J = σ E, reinforcing the proportional relationship.

Why Other Options Are Wrong:

Claiming the statements are false contradicts basic transport models; denying the explanatory role of mobility ignores the definition μ = v_d / E.

Common Pitfalls:

Extending linearity into high-field regimes without accounting for velocity saturation; confusing thermal velocity with drift velocity.

Final Answer:

Both A and R are true and R is correct explanation of A