The potential difference between two points is 20 V. How much work will be done in carrying a charge of `400 mu` from one point to the other?

Options

A. `3xx10^2J`
B. `5xx10^4J`
C. `8xx10^-3J`
D. `9xx10^6J`

Answer

To solve the problem of how much work is done in carrying a charge of 400 microcoulombs across a potential difference of 20 volts, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the given values**:
- Potential difference (V) = 20 volts
- Charge (Q) = 400 microcoulombs = \( 400 \times 10^{-6} \) coulombs

2. **Use the formula for work done (W)**:
The work done in moving a charge in an electric field is given by the formula:
\[ W = Q \cdot V \]
where:
- \( W \) is the work done,
- \( Q \) is the charge,
- \( V \) is the potential difference.

3. **Substitute the values into the formula**:
\[ W = (400 \times 10^{-6} \, \text{C}) \cdot (20 \, \text{V}) \]

4. **Calculate the work done**:
\[ W = 8000 \times 10^{-6} \, \text{J} \]
\[ W = 8 \times 10^{-3} \, \text{J} \]

5. **Final answer**:
The work done in carrying the charge from one point to another is \( 8 \times 10^{-3} \, \text{J} \) or 0.008 J.