Question

A current of 2 A flows through a wire of crosssectional area 25.0 mm2 . The number of free electrons in a cubic meter are 2.0 x 10²⁸ . The drift velocity of the electrons is _____ x 10^-6 ms^-1 (Given, charge on electron = 1.6 x 10^-19C)

Hint:

Drift velocity is typically very small due to the high number of free electrons.

Answer 1

Correct Answer: 25

Step 1: Use the formula for drift velocity - Drift velocity is given by: \[ V_d = \frac{I}{n e A}, \] where \(I\) is the current, \(n\) is the number of free electrons per unit volume, \(e\) is the electron charge, and \(A\) is the cross-sectional area.

Step 2: Substitute the values - \[ V_d = \frac{2}{(2 \times 10^{28}) \cdot (1.6 \times 10^{-19}) \cdot (25 \times 10^{-6})}. \] Simplifying: \[ V_d = \frac{2}{800 \times 10^{-6}} = 25 \times 10^{-6} \, \text{m/s}. \]

Final Answer: The drift velocity of the electrons is 25 × 10⁻⁶ m/s.