Question

Solve the following problem.

The magnitude of current density in a copper wire is 500 A/cm². If the number of free electrons per cm³ of copper is 8.47 × 10²² calculate the drift velocity of the electrons through the copper wire (charge on an e = 1.6 × 10^-19 C)

Answer 1

Given: J = 500 A/cm² = 500 × 10⁴ A/m², n = 8.47 × 10²² electrons/cm³ = 8.47 × 10²⁸ electrons/m³
e = 1.6 × 10^-19 C

To find: Drift velocity (v_d)

Formula: v_d = `"J"/"ne"`

Calculation: From formula.

v_d = `(500xx10^4)/(8.47xx10^28xx1.6xx10^-19)`

= `500/(8.47xx1.6)xx10^-5`

= {antilog [log 500 − log 8.47 − log 1.6]} × 10⁻⁵

= {antilog [2.6990 − 0.9279 − 0.2041]} × 10⁻⁵

= {antilog [1.5670]} × 10⁻⁵

= 3.690 × 10¹ × 10⁻⁵

= 3.69 × 10⁻⁴ m/s

The drift velocity of electrons is 3.69 × 10⁻⁴ m/s.