15 joule of work has to be done against an existing electric field to take a charge of 0.01 C from A to B. Then the potential difference `(V_(B) - V_(A))` is :-

Options

A. 1500 volt
B. `-1500` volt
C. `0.15` volt
D. none of these

Answer

To find the potential difference \( V_B - V_A \) when 15 joules of work is done against an electric field to move a charge of 0.01 C from point A to point B, we can use the formula relating work done, charge, and potential difference.

### Step-by-Step Solution:

1. **Understand the relationship between work, charge, and potential difference**:
The work done \( W \) in moving a charge \( Q \) through a potential difference \( V_B - V_A \) is given by the equation:
\[ W = Q \cdot (V_B - V_A) \]

2. **Substitute the known values**:
We know that:
- Work done \( W = 15 \) joules
- Charge \( Q = 0.01 \) C

Substituting these values into the equation:
\[ 15 = 0.01 \cdot (V_B - V_A) \]

3. **Rearranging the equation to find the potential difference**:
To isolate \( V_B - V_A \), we can divide both sides of the equation by \( 0.01 \):
\[ V_B - V_A = \frac{15}{0.01} \]

4. **Calculate the potential difference**:
Performing the division:
\[ V_B - V_A = 1500 \text{ volts} \]

5. **Conclusion**:
The potential difference \( V_B - V_A \) is \( 1500 \) volts.

### Final Answer:
\[ V_B - V_A = 1500 \text{ volts} \]