Relating current to the total number of charge carriers via drift speed Steps: - Current I equals the product of charge per carrier e, number density n, cross-sectional area A, and drift speed v_d: I = n e A v_d. - Total free electrons N = n × volume = n A L, where L is wire length. - Substitute n A from the current formula: n A = I / (e v_d), so N = [I / (e v_d)] × L. - Plug in values with e = 1.6 × 10^{-19} C: N = [2 / (1.6 × 10^{-19} × 5.0 × 10^{-4})] × 0.35 = 5.3 × 10^{17}. Why B is correct: - It matches N from the charge carrier formula I = N e v_d / L, derived from steady-state current flow. Why the others are wrong: - A underestimates by factor of ~40, likely from omitting L or miscalculating e v_d. - C overestimates by factor of ~3, possibly from rounding error in e or v_d. - D overestimates by factor of ~80, perhaps confusing with …