A 2 ampere current flows in a uniform conductor which has 1 x 10^24 free electrons per metre. What is their average drift velocity?

Steps to Solve

1. Understand the relationship for current and drift velocity

   The average drift velocity ( v_d ) can be calculated using the formula: $$ I = n e A v_d $$ where:

   • ( I ) is the current (in amperes),
   • ( n ) is the number of free electrons per unit volume (in ( m^{-3} )),
   • ( e ) is the charge of an electron (( 1.6 \times 10^{-19} , \text{C} )),
   • ( A ) is the cross-sectional area of the conductor (in ( m^2 )),
   • ( v_d ) is the average drift velocity (in ( m/s )).

   In this scenario, we can assume ( A ) cancels out or is normalized if only average drift velocity is needed.

2. Rearranging the formula to solve for drift velocity

   Rearranging the above formula gives: $$ v_d = \frac{I}{n e A} $$ For simplicity, we will ignore ( A ) since it is not provided, so we focus on the ratio ( \frac{I}{n e} ).

3. Insert the known values

   Substituting the known values into the formula, we have:

   • ( I = 2 , \text{A} )
   • ( n = 1 \times 10^{24} , \text{m}^{-3} )
   • ( e = 1.6 \times 10^{-19} , \text{C} )

   Thus: $$ v_d = \frac{2}{(1 \times 10^{24}) \times (1.6 \times 10^{-19})} $$

4. Calculate the drift velocity

   Perform the calculation: $$ v_d = \frac{2}{1.6 \times 10^{5}} = 1.25 \times 10^{-5} , \text{m/s} $$