Question

A small but measurable current of 1.2ʠ10 10 A exists in a copper wire whose diameter is 2.5 mm. If the charge carrier density in copper is 8.47(1028 electrons per cubic meter, calculate the electron drift speed

Answer 1

Solution :

Given :

Current (i) = 1.2 x 10^-10 A

Diameter of wire (d) = 2.5 mm

Thus : Radius of wire (r) = d / 2 = 1.25 mm = 1.25 x 10^-3 m

So, Area of cross section of wire (A) = π r² =π (1.25 x 10^-3 m)² = 4.91 x 10 ^-6 m²

And, Current density (J) = i / A = (1.2 x 10^-10 A) / (4.91 x 10 ^-6 m²) = 2.44 x 10^-5 A/m²

Here, The number of charge carriers per unit volume (n) = 8.47 x 10 ²⁸ m^-3

Charge (q) = 1.6 x 10^-19 C

Therefore: Drift speed (V_drift) = J / n q = (2.44 x 10^-5 A/m²) / {(1.6 x 10^-19 C)(8.47 x 10 ²⁸ m^-3)} = 1.804 x 10^-15 m/s