When a current flows in a conductor, the order of magnitude of drift velocity of electrons through it is :

Options

A. `10^(10)cm//s`
B. `10^(4)cm//s`
C. `10^(-2) cm//s`
D. `10^(-7)cm//s`

Answer

To determine the order of magnitude of the drift velocity of electrons in a conductor when a current flows through it, we can follow these steps:

### Step 1: Understand the formula for drift velocity
The drift velocity \( v_d \) of electrons in a conductor can be expressed using the formula:
\[ v_d = \frac{J}{n \cdot e} \]
where:
- \( J \) is the current density,
- \( n \) is the number density of charge carriers (electrons),
- \( e \) is the charge of an electron.

### Step 2: Define the parameters
For a copper wire with a cross-sectional area of \( A = 1 \, \text{mm}^2 = 1 \times 10^{-6} \, \text{m}^2 \) carrying a current \( I = 1 \, \text{A} \):
- The current density \( J \) can be calculated as:
\[ J = \frac{I}{A} = \frac{1 \, \text{A}}{1 \times 10^{-6} \, \text{m}^2} = 1 \times 10^{6} \, \text{A/m}^2 \]

### Step 3: Determine the number density of electrons
For copper, the number density \( n \) of conduction electrons is approximately:
\[ n \approx 8.5 \times 10^{28} \, \text{electrons/m}^3 \]

### Step 4: Use the charge of an electron
The charge \( e \) of an electron is:
\[ e \approx 1.6 \times 10^{-19} \, \text{C} \]

### Step 5: Substitute values into the drift velocity formula
Now we can substitute the values into the drift velocity formula:
\[ v_d = \frac{1 \times 10^{6} \, \text{A/m}^2}{(8.5 \times 10^{28} \, \text{electrons/m}^3) \cdot (1.6 \times 10^{-19} \, \text{C})} \]

### Step 6: Calculate the drift velocity
Calculating the denominator:
\[ n \cdot e = (8.5 \times 10^{28}) \cdot (1.6 \times 10^{-19}) \approx 1.36 \times 10^{10} \, \text{C/m}^3 \]
Now substituting back:
\[ v_d = \frac{1 \times 10^{6}}{1.36 \times 10^{10}} \approx 7.35 \times 10^{-5} \, \text{m/s} \]

### Step 7: Convert to appropriate units
Converting to centimeters per second:
\[ v_d \approx 7.35 \times 10^{-5} \, \text{m/s} = 7.35 \times 10^{-3} \, \text{cm/s} \approx 10^{-4} \, \text{m/s} \]

### Conclusion
The order of magnitude of the drift velocity of electrons in a conductor carrying a current of 1 A is approximately:
\[ \boxed{10^{-4} \, \text{m/s}} \text{ or } 10^{-2} \, \text{cm/s} \]