When a negative charge moves in a direction opposite to the direction of an electric field,

Options

A. The field does work on the charge
B. The charge does work on the field
C. The charge gains potential energy
D. The charge loses potential energy

Answer

To solve the question regarding the movement of a negative charge in an electric field, we can break it down into a series of logical steps:

### Step-by-Step Solution:

1. **Understanding the Electric Field**:
- An electric field (E) is defined as the region around a charged object where other charges experience a force. The direction of the electric field is from positive to negative charges.

2. **Identifying the Charge and Its Movement**:
- In this scenario, we have a negative charge (let's denote it as -Q) moving in a direction opposite to the electric field. If the electric field is directed to the right, the negative charge is moving to the left.

3. **Applying Coulomb's Law**:
- According to Coulomb's law, the force (F) experienced by a charge in an electric field is given by \( F = Q \cdot E \). For a negative charge, the force will be \( F = -Q \cdot E \). This indicates that the force on the negative charge will be in the opposite direction to the electric field.

4. **Analyzing the Work Done**:
- Work (W) done by a force is calculated using the formula \( W = F \cdot d \cdot \cos(\theta) \), where \( d \) is the displacement and \( \theta \) is the angle between the force and displacement vectors.
- Since the force on the negative charge is in the opposite direction to the electric field, and the charge is moving in the opposite direction to the electric field, the work done by the electric field on the charge is positive.

5. **Potential Energy Consideration**:
- The potential energy (U) of a charge in an electric field is given by \( U = -Q \cdot V \), where V is the electric potential.
- As the negative charge moves against the electric field (from lower potential to higher potential), its potential energy increases. Therefore, the charge gains potential energy.

6. **Conclusion**:
- Based on the analysis, we conclude that:
- The electric field does work on the charge (Option A is correct).
- The charge gains potential energy (Option D is correct).
- Therefore, the correct options are A and D.