Drift velocity of free electrons when current passes through the conductor is of the order of

Options

A. `10 mm//s`
B. `10 m//s`
C. `10 km//s`
D. `10^(6) m//s`

Answer

To determine the drift velocity of free electrons when current passes through a conductor, we can use the formula for drift velocity (V_d):

\[ V_d = \frac{I}{n \cdot A \cdot e} \]

Where:
- \( I \) = current (in amperes)
- \( n \) = number of free electrons per unit volume (in electrons/m³)
- \( A \) = cross-sectional area of the conductor (in m²)
- \( e \) = charge of an electron (approximately \( 1.6 \times 10^{-19} \) coulombs)

### Step-by-Step Solution:

1. **Identify the Values**:
- Let's assume a current \( I = 1.6 \, \text{A} \) (this is a reasonable value for calculations).
- The number density of free electrons \( n \) is approximately \( 10^{27} \, \text{electrons/m}^3 \).
- The cross-sectional area \( A \) is taken as \( 1 \, \text{mm}^2 \), which is equal to \( 1 \times 10^{-6} \, \text{m}^2 \).

2. **Substitute the Values into the Formula**:
\[ V_d = \frac{1.6}{(10^{27}) \cdot (1 \times 10^{-6}) \cdot (1.6 \times 10^{-19})} \]

3. **Calculate the Denominator**:
- Calculate \( n \cdot A \cdot e \):
\[ n \cdot A \cdot e = (10^{27}) \cdot (1 \times 10^{-6}) \cdot (1.6 \times 10^{-19}) = 1.6 \times 10^{2} \, \text{(after simplifying)} \]

4. **Calculate Drift Velocity**:
\[ V_d = \frac{1.6}{1.6 \times 10^{2}} = 10^{-2} \, \text{m/s} \]

5. **Convert to Appropriate Units**:
- \( 10^{-2} \, \text{m/s} = 0.01 \, \text{m/s} = 1 \, \text{cm/s} = 10 \, \text{mm/s} \)

6. **Conclusion**:
- The drift velocity of free electrons when current passes through a conductor is of the order of \( 10 \, \text{mm/s} \).