Drift Velocity Calculator
Enter conductivity σ, carrier density n and charge q to compute the drift velocity v = μE = σE/(nq) under an applied field E.
輸入資料
計算結果
重點速覽：In a conductor, free carriers are pushed by an electric field and acquire a small average drift speed v opposite to E. Mobility μ = σ/(nq) links them: v = μE = σE/(nq). Despite the tiny carrier speed, the electromagnetic signal travels near light speed, so a lamp lights instantly although electrons barely move. This resolves the common confusion between signal speed and carrier drift speed.
計算公式
Drift velocity: v = σE/(nq).
Mobility: μ = σ/(nq).
Current density: J = nqv = σE.
$$v = \frac{\sigma E}{nq}$$$$\mu = \frac{\sigma}{nq}$$$$J = nqv = \sigma E$$使用說明
- Enter conductivity σ, carrier density n, charge q and field E.
- The tool returns drift velocity v and mobility μ.
固定 I=1 A、q=e、r=1 mm（A≈3.1416e-6 m²），不同 n 的漂移速度
| 材料/濃度 | n (m⁻³) | v_d (mm/s) | v_d (m/s) | 走 1 m 時間 | J (A/m²) |
|---|---|---|---|---|---|
| Cu | 8.47e28 | 0.0234 | 2.34e-5 | 11.9 小時 | 3.18e5 |
| Al | 1.81e29 | 0.0109 | 1.09e-5 | 25.4 小時 | 3.18e5 |
| 弱 n-type Si | 1e23 | 19.87 | 0.01987 | 50.3 秒 | 3.18e5 |
| 中 n-type Si | 1e21 | 1987 | 1.987 | 0.503 秒 | 3.18e5 |
| 高 n-type Si | 1e20 | 19870 | 19.87 | 0.050 秒 | 3.18e5 |
理財情境案例
Copper wire at 0.01 V/m
σ=5.8×10⁷, n=8.5×10²⁸, q=1.602×10⁻¹⁹, E=0.01 V/m.
v = 5.8e7×0.01/(8.5e28×1.602e-19) ≈ 4.3×10⁻⁴ m/s.
Carriers drift ≈ 0.43 mm/s while the signal moves near light speed.
常見問題
Why do lights turn on instantly if drift is so slow?
The electric field propagates at near light speed, pushing carriers everywhere almost at once; the drift speed is just the average carrier creep, not the signal speed.
What is mobility?
Mobility μ = σ/(nq) is how fast carriers drift per unit field; higher mobility means faster drift for the same field.
相關工具
參考資料
Content reviewed by the Hong Kong Calculator science team. Drift velocity and Drude model verified against Halliday/Serway introductory physics and electromagnetism texts and the DSE Physics curriculum.