Drift velocity from current and electron density

Steps:

• Calculate current I = V/R = 6.0/15 = 0.40 A.
• Compute cross-sectional area A = π(r)^2, with r = 1.5 × 10^{-3} m, so A = π(1.5 × 10^{-3})^2 = 7.07 × 10^{-6} m².
• Use drift speed formula v_d = I / (n e A), where e = 1.6 × 10^{-19} C, n = 10^{28} m^{-3}.
• Substitute: v_d = 0.40 / (10^{28} × 1.6 × 10^{-19} × 7.07 × 10^{-6}) = 3.9 × 10^{-5} m s^{-1}.

Why B is correct:

• Matches v_d = I/(n e A), the standard formula linking current to electron drift in conductors.

Why the others are wrong:

• A: Underestimates by factor of ~4, likely from incorrect area or e value.
• C: Overestimates by ~1.6, possibly from using diameter instead of radius in A.
• D: Too small by ~16, perhaps from missing current or using wrong n.

Final answer: B