A charge is moved against repulsion.Then there is

Options

A. decreasing its kinetic energy
B. increasing its potential energy
C. increasing both the energies
D. decreasing both the energies

Answer

To solve the problem regarding a charge being moved against repulsion, we will follow these steps:

### Step-by-Step Solution:

1. **Identify the Charges**:
Let's consider two positive charges, \( q_1 \) and \( q_2 \). Since both charges are positive, they will repel each other.

2. **Direction of Force**:
When one charge is moved against the repulsion, the force \( F \) acting on the moving charge \( q_2 \) due to the other charge \( q_1 \) will be directed away from \( q_1 \).

3. **Work Done Calculation**:
The work done \( W \) when moving a charge in an electric field can be calculated using the formula:
\[ W = F \cdot s \cdot \cos(\theta) \]
where:
- \( F \) is the force,
- \( s \) is the displacement,
- \( \theta \) is the angle between the force and the displacement.

4. **Determine the Angle**:
Since the charge is being moved against the force of repulsion, the angle \( \theta \) between the force \( F \) and the displacement \( s \) is \( 180^\circ \). Therefore, we have:
\[ \cos(180^\circ) = -1 \]

5. **Substituting the Angle**:
Substituting this value into the work done equation gives:
\[ W = F \cdot s \cdot (-1) = -F \cdot s \]
This indicates that the work done is negative.

6. **Implications of Negative Work Done**:
According to the work-energy theorem, the work done on an object is equal to the change in its kinetic energy. If the work done is negative, it implies that the kinetic energy of the moving charge is decreasing.

7. **Potential Energy Consideration**:
The potential energy \( U \) in an electric field is related to the work done. Since the work done is negative, the potential energy of the system is increasing. This is because moving against the electric field requires energy input, which increases the potential energy.

8. **Conclusion**:
Based on the analysis:
- The kinetic energy of the moving charge is decreasing.
- The potential energy of the system is increasing.

### Final Answer:
- **Correct Statements**:
- The kinetic energy is decreasing (Option A).
- The potential energy is increasing (Option B).