The drift velocity of free electrons in a conductor of length 6 m is 0.25 `ms^(-1)` under the application of potential difference of 100 V. The mobility of free electrons is

Options

A. `2 * 10^(-3) m^2 V^(-1) s^(-1)`
B. `2.5 * 10^(-2) m^2 V^(-1) s^(-1)`
C. `1.5 * 10^(-2) m^2 V^(-1) s^(-1)`
D. `1.5 * 10^(-3) m^2 V^(-1) s^(-1)`

Answer

To find the mobility of free electrons in a conductor, we can use the relationship between drift velocity, electric field, and mobility. Here’s the step-by-step solution:

### Step 1: Identify the given values
- Length of the conductor (L) = 6 m
- Drift velocity (v_d) = 0.25 m/s
- Potential difference (V) = 100 V

### Step 2: Calculate the electric field (E)
The electric field (E) in the conductor can be calculated using the formula:
\[ E = \frac{V}{L} \]
Substituting the known values:
\[ E = \frac{100 \, \text{V}}{6 \, \text{m}} \]
\[ E = 16.67 \, \text{V/m} \]

### Step 3: Use the relationship between drift velocity and mobility
The drift velocity (v_d) is related to the mobility (μ) and the electric field (E) by the formula:
\[ v_d = \mu \cdot E \]
Rearranging this formula to solve for mobility (μ):
\[ \mu = \frac{v_d}{E} \]

### Step 4: Substitute the values to find mobility
Now, substituting the values of drift velocity and electric field:
\[ \mu = \frac{0.25 \, \text{m/s}}{16.67 \, \text{V/m}} \]
Calculating this gives:
\[ \mu = 0.015 \, \text{m}^2/\text{V}\cdot\text{s} \]
or
\[ \mu = 1.5 \times 10^{-2} \, \text{m}^2/\text{V}\cdot\text{s} \]

### Final Answer
The mobility of free electrons is:
\[ \mu = 1.5 \times 10^{-2} \, \text{m}^2/\text{V}\cdot\text{s} \]

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