A potential difference of 4.5 V is applied across a conductor of length 0.1 m. If the drift velocity of electrons is `1.5 xx10^(-4)ms^(-1)`, find the electrons mobility. 

Answer

To find the electron mobility given the potential difference, length of the conductor, and drift velocity, we can follow these steps:

### Step 1: Understand the relationship between drift velocity, electric field, and mobility
The drift velocity \( v_d \) of electrons in a conductor is given by the formula:
\[ v_d = \mu E \]
where:
- \( \mu \) is the electron mobility,
- \( E \) is the electric field.

### Step 2: Calculate the electric field \( E \)
The electric field \( E \) can be calculated using the formula:
\[ E = \frac{V}{L} \]
where:
- \( V \) is the potential difference (4.5 V),
- \( L \) is the length of the conductor (0.1 m).

Substituting the values:
\[ E = \frac{4.5 \, \text{V}}{0.1 \, \text{m}} = 45 \, \text{V/m} \]

### Step 3: Rearrange the drift velocity formula to solve for mobility \( \mu \)
From the drift velocity equation, we can rearrange it to find \( \mu \):
\[ \mu = \frac{v_d}{E} \]

### Step 4: Substitute the values into the mobility formula
Now, substitute the known values:
- \( v_d = 1.5 \times 10^{-4} \, \text{m/s} \)
- \( E = 45 \, \text{V/m} \)

So, we have:
\[ \mu = \frac{1.5 \times 10^{-4} \, \text{m/s}}{45 \, \text{V/m}} \]

### Step 5: Perform the calculation
Calculating the above expression:
\[ \mu = \frac{1.5 \times 10^{-4}}{45} = 3.33 \times 10^{-6} \, \text{m}^2/\text{V s} \]

### Final Answer
The mobility of electrons is:
\[ \mu = 3.33 \times 10^{-6} \, \text{m}^2/\text{V s} \]

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