Find the work done by some external force in moving a charge `q=4 muC` from infinity to a point, where electric potential is `10^(4)V`

Options

A. `4 xx 10^(-2)J`
B. `2 xx 10^(-2)J`
C. `8 xx 10^(-2)J`
D. `1xx 10^(-2)J`

Answer

To find the work done by an external force in moving a charge \( q = 4 \, \mu C \) from infinity to a point where the electric potential is \( 10^4 \, V \), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Given Values**:
- The charge \( q = 4 \, \mu C = 4 \times 10^{-6} \, C \).
- The electric potential at the point \( V = 10^4 \, V \).
- At infinity, the electric potential \( V_{\text{initial}} = 0 \, V \).

2. **Formula for Work Done**:
The work done \( W \) in moving a charge in an electric field is given by the formula:
\[ W = q \times (V_{\text{final}} - V_{\text{initial}}) \]

3. **Substitute the Values**:
- Here, \( V_{\text{final}} = 10^4 \, V \) and \( V_{\text{initial}} = 0 \, V \).
- Substitute these values into the formula:
\[ W = q \times (10^4 - 0) \]
\[ W = 4 \times 10^{-6} \, C \times 10^4 \, V \]

4. **Calculate the Work Done**:
\[ W = 4 \times 10^{-6} \times 10^4 = 4 \times 10^{-2} \, J \]

5. **Final Result**:
Thus, the work done by the external force in moving the charge from infinity to the point is:
\[ W = 4 \times 10^{-2} \, J \]

### Conclusion:
The work done in moving the charge is \( 4 \times 10^{-2} \, J \), which corresponds to option A.

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