Drift Speed Proportional to Current

Steps:

• Electric current I equals charge flow rate: I = n e A v_d, where n is charge carrier density, e is electron charge, A is cross-sectional area, and v_d is average drift speed.
• For a given wire material and size, n and e are fixed, and A is constant.
• Rearrange formula: v_d = I / (n e A).
• Thus, v_d is directly proportional to I.

Why D is correct:

• From the current formula I = n e A v_d, drift speed v_d ∝ I for fixed n, e, and A.

Why the others are wrong:

• A: Specific value like 3 × 10^{-4} m/s applies only to typical household currents; not generally true without conditions.
• B: v_d ∝ 1/A, so inversely proportional to area.
• C: Length L does not appear in the drift speed formula; v_d independent of L for given I.

Final answer: D