A charge of `5 mu C` is placed at the center of a square `ABCD` of side `10 cm`. Find the work done `("in" mu J)` in moving a charge of `1 mu C` from A to B.

Explanation

To solve the problem of finding the work done in moving a charge of \(1 \mu C\) from point A to point B in the presence of a charge of \(5 \mu C\) at the center of a square ABCD, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Configuration**:
- We have a square ABCD with a side length of \(10 \, cm\) (or \(0.1 \, m\)).
- A charge of \(5 \mu C\) is placed at the center of the square.
- We need to find the work done in moving a charge of \(1 \mu C\) from point A to point B.

2. **Calculate the Electric Potential at Points A and B**:
- The electric potential \(V\) due to a point charge is given by the formula:
\[ V = \frac{k \cdot Q}{r} \]
where \(k\) is Coulomb's constant (\(8.99 \times 10^9 \, N \cdot m^2/C^2\)), \(Q\) is the charge, and \(r\) is the distance from the charge to the point where the potential is being calculated.

3. **Determine the Distance from the Center to Points A and B**:
- The distance from the center of the square to any vertex (like A or B) can be calculated using the Pythagorean theorem. The distance from the center to a vertex is:
\[ r = \frac{\sqrt{(0.1)^2 + (0.1)^2}}{2} = \frac{\sqrt{0.02}}{2} = \frac{0.1\sqrt{2}}{2} = 0.05\sqrt{2} \, m \approx 0.0707 \, m \]

4. **Calculate the Electric Potential at Points A and B**:
- Since both points A and B are equidistant from the charge at the center, the potentials at A and B will be the same:
\[ V_A = V_B = \frac{k \cdot 5 \times 10^{-6}}{0.0707} \]

5. **Calculate the Work Done in Moving the Charge**:
- The work done \(W\) in moving a charge \(q\) in an electric field is given by:
\[ W = q \cdot (V_B - V_A) \]
- Since \(V_A = V_B\), we have:
\[ W = 1 \times 10^{-6} \cdot (V_B - V_A) = 1 \times 10^{-6} \cdot 0 = 0 \]

6. **Conclusion**:
- The work done in moving the charge \(1 \mu C\) from A to B is \(0 \, \mu J\).

### Final Answer:
The work done in moving the charge from A to B is \(0 \, \mu J\).