Relation between Current and Drift Velocity: Practice Problem & Solution

Solution Explained:

To solve this problem, we apply the core principles of Relation between Current and Drift Velocity. Understanding the underlying formula is key to arriving at the correct answer below:

To find the drift velocity

$v_d$

of the electrons, we use the formula for current in terms of drift velocity:

$$I = n A e v_d$$

Where:

• 
  $I$ 

  is the current (1.2 A),

• 
  $n$ 

  is the number of free electrons per unit volume ( $5 \times 10^{28} \, \text{m}^{-3}$ 

  ),

• 
  $A$ 

  is the cross-sectional area of the conductor ( $10^{-4} \, \text{m}^2$ 

  ),

• 
  $e$ 

  is the charge of an electron ( $1.6 \times 10^{-19} \, \text{C}$ 

  ),

• 
  $v_d$ 

  is the drift velocity of the electrons (which we need to calculate).

Step 1: Rearranging the formula to solve for $v_d$

$$v_d = \frac{I}{n A e}$$

Step 2: Substituting the given values

$$v_d = \frac{1.2}{(5 \times 10^{28}) \times (10^{-4}) \times (1.6 \times 10^{-19})}$$

Step 3: Performing the calculation

$$v_d = \frac{1.2}{(5 \times 10^{28}) \times (10^{-4}) \times (1.6 \times 10^{-19})}$$

$$v_d = \frac{1.2}{8 \times 10^{6}}$$

$$v_d = 1.5 \times 10^{-7} \, \text{m/s}$$

Final Answer:

The drift velocity of the electrons is

$\boxed{1.5 \times 10^{-7} \, \text{m/s}}$

.