Two charges `q_(1) = 3.0 mu C` and `q_(2) = - 4.0 mu C` initiallly are separated by a distance `r_(0) = 2.0 cm `. An external agent moves the charges until they are `r_(f) = 5.0 cm ` apart. How much work is done by the electric field in moving the charges from `r_(0) ` to `r_(f)` ? Is the work positive or negative ?

Explanation

To find the work done by the electric field in moving the charges from an initial distance \( r_0 \) to a final distance \( r_f \), we can use the concept of electric potential energy. The work done by the electric field is equal to the change in potential energy of the system.

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Charge \( q_1 = 3.0 \, \mu C = 3.0 \times 10^{-6} \, C \)
- Charge \( q_2 = -4.0 \, \mu C = -4.0 \times 10^{-6} \, C \)
- Initial distance \( r_0 = 2.0 \, cm = 2.0 \times 10^{-2} \, m \)
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