Dimensional Analysis of Mobility Formula

Steps:

• Electron charge e has SI base unit ampere-second, A s.
• Electron mass m has SI base unit kilogram, kg.
• Collision time τ has SI base unit second, s.
• Thus, μ = (e / m) τ has units (A s / kg) × s = A s² kg⁻¹.

Why B is correct:

• The Drude model formula μ = e τ / m derives SI base units A s kg^{-1} from charge (A s), divided by mass (kg), multiplied by time (s), combining to match B.

Why the others are wrong:

• A lacks ampere unit from charge.
• C lacks ampere unit from charge.
• D has inverse second, contradicting time contributions from e and τ.

Final answer: B