Problem 1: Drift Velocity

Given: Copper wire, n = $8.5 \times 10^{28}$ /$m^{3}$, A = 1 $mm^{2}$ = $1 \times 10^{-6}$ $m^{2}$, I = 1 A

Find: Drift velocity vd

Step 1 — Identify formula: $v_d = \frac{I}{neA}$

Step 2 — Substitute with units: $v_d = \frac{1 \text{ A}}{(8.5 \times 10^{28} \text{ m}^{-3})(1.6 \times 10^{-19} \text{ C})(1 \times 10^{-6} \text{ m}^2)}$

Step 3 — Calculate denominator: $neA = 8.5 \times 1.6 \times 10^{28-19-6} \text{ A·s/m} = 13.6 \times 10^3 \text{ C/m} = 1.36 \times 10^4 \text{ C/m}$

Step 4 — Final result: $v_d = \frac{1}{1.36 \times 10^4} \text{ m/s} \approx 7.35 \times 10^{-5} \text{ m/s}$

Answer: vd ≈ $7.35 \times 10^{-5}$ m/s ≈ 0.074 mm/s (extremely slow)