A particle moves in a gravity free space where an electric field of strength E and a magnetic field of induction B exit. Which of the following statement is are correct?

Options

A. If `E!=0 and B!=0`, velocity of the particle may remains constant
B. If E=0, the particle cannot trace a circular path
C. If E=0, the kinetic energy of the particle remains constant
D. None of these

Explanation

To determine which statements are correct regarding a particle moving in a gravity-free space with an electric field (E) and a magnetic field (B), we will analyze each statement step by step.

### Step-by-Step Solution:

1. **Understanding the Forces:**
- A charged particle in an electric field experiences an electric force given by \( F_E = qE \), where \( q \) is the charge of the particle.
- In a magnetic field, the magnetic force acting on a moving charged particle is given by \( F_B = q(\mathbf{v} \times \mathbf{B}) \), where \( \mathbf{v} \) is the velocity of the particle and \( \mathbf{B} \) is the magnetic field.

2. **Analyzing Statement A:**
- Statement A claims that the velocity of the particle may remain constant.
- This is possible if the electric force and magnetic force are equal in magnitude and opposite in direction, resulting in a net force of zero.
- If \( F_E = F_B \), then \( qE = q(\mathbf{v} \times \mathbf{B}) \). If these forces balance, the particle will have constant velocity.
- **Conclusion:** Statement A is **true**.

3. **Analyzing Statement B:**
- Statement B claims that if \( E = 0 \), the particle cannot trace a circular path.
- A circular path is traced when the magnetic force is perpendicular to the velocity of the particle. The electric field does not influence the ability to trace a circular path if the magnetic field is present.
- Therefore, even if \( E = 0 \), the particle can still move in a circular path due to the magnetic force.
- **Conclusion:** Statement B is **false**.

4. **Analyzing Statement C:**
- Statement C claims that if \( E = 0 \), the kinetic energy of the particle remains constant.
- If \( E = 0 \), the only force acting on the particle is the magnetic force, which does no work since it is always perpendicular to the velocity of the particle.
- According to the work-energy theorem, if no work is done, the kinetic energy remains constant.
- **Conclusion:** Statement C is **true**.

5. **Analyzing Statement D:**
- Statement D claims that none of the above statements are correct.
- Since we have established that Statements A and C are true, Statement D is incorrect.
- **Conclusion:** Statement D is **false**.

### Final Summary:
- The correct statements are:
- Statement A: **True**
- Statement B: **False**
- Statement C: **True**
- Statement D: **False**

Thus, the correct options are A and C.