To solve the question, we need to analyze the conditions under which a charged particle can move in a gravity-free space without a change in velocity. This implies that the net force acting on the particle must be zero, which means there is no acceleration. Let's go through the options step by step.
### Step-by-Step Solution:
1. **Understanding the Scenario**:
- A charged particle is moving in a gravity-free space.
- The velocity of the particle is constant, which means there is no net force acting on it (Newton's first law).
2. **Analyzing Each Option**:
- **Option 1**: Electric field (E) = 0 and Magnetic field (B) ≠ 0.
- If E = 0, the electric force (F_e = Q * E) is also 0.
- The magnetic force (F_m = Q * V × B) can be 0 if the angle between V and B is 0 (i.e., they are parallel).
- Therefore, if both forces are zero, the net force is zero, and this option is possible.
- **Option 2**: Electric field (E) = 0 and Magnetic field (B) ≠ 0.
- If E = 0, then F_e = 0.
- The magnetic force can also be zero if the velocity is parallel to the magnetic field (θ = 0).
- Thus, the net force can still be zero, making this option possible.
- **Option 3**: Electric field (E) ≠ 0 and Magnetic field (B) = 0.
- If E ≠ 0, then F_e = Q * E is not zero.
- With no magnetic field to counteract this force, the net force cannot be zero.
- Therefore, this option is not possible.
- **Option 4**: Electric field (E) ≠ 0 and Magnetic field (B) ≠ 0.
- Here, both forces are present: F_e = Q * E and F_m = Q * V × B.
- It is possible for these two forces to be equal in magnitude and opposite in direction, resulting in a net force of zero.
- Therefore, this option is also possible.
3. **Conclusion**:
- The options that are possible for a charged particle moving in a gravity-free space without a change in velocity are:
- **Option 1**: E = 0, B ≠ 0
- **Option 2**: E = 0, B ≠ 0
- **Option 4**: E ≠ 0, B ≠ 0
- Thus, the correct options are 1, 2, and 4.
### Final Answer:
The possible scenarios are **Option 1, Option 2, and Option 4**.
