In the potentiometer experiment, electron in the potentiometer wire experiences a force `4.8 xx 10^(-19) N`. The length of potentiometer wire is 4 m. The emf of the battery connected across the potentiometer wire is [given, `e = 1.6 xx 10^(-19)C`]

Options

A. 12 V
B. 9 V
C. 16 V
D. 6 V

Explanation

To solve the problem, we need to find the EMF (electromotive force) of the battery connected across the potentiometer wire, given the force experienced by an electron in the wire, the length of the wire, and the charge of the electron.

### Step-by-Step Solution:

1. **Identify the given values:**
- Force on the electron, \( F = 4.8 \times 10^{-19} \, \text{N} \)
- Length of the potentiometer wire, \( L = 4 \, \text{m} \)
- Charge of the electron, \( e = 1.6 \times 10^{-19} \, \text{C} \)

2. **Use the formula for the force on a charged particle in an electric field:**
\[ F = e \cdot E \]
where \( E \) is the electric field.

3. **Relate the electric field to the EMF and the length of the wire:**
The electric field \( E \) can be expressed as:
\[ E = \frac{V}{L} \]
where \( V \) is the EMF of the battery.

4. **Substitute the expression for \( E \) into the force equation:**
\[ F = e \cdot \frac{V}{L} \]

5. **Rearrange the equation to solve for \( V \):**
\[ V = \frac{F \cdot L}{e} \]

6. **Substitute the known values into the equation:**
\[ V = \frac{(4.8 \times 10^{-19} \, \text{N}) \cdot (4 \, \text{m})}{1.6 \times 10^{-19} \, \text{C}} \]

7. **Calculate the numerator:**
\[ 4.8 \times 10^{-19} \, \text{N} \cdot 4 \, \text{m} = 19.2 \times 10^{-19} \, \text{N m} \]

8. **Now calculate \( V \):**
\[ V = \frac{19.2 \times 10^{-19}}{1.6 \times 10^{-19}} = 12 \, \text{V} \]

9. **Conclusion:**
The EMF of the battery connected across the potentiometer wire is \( 12 \, \text{V} \).