A charged particle moves in a gravity-free space without change in velocity. Which of the following is/are possible?
(i) `E = 0, B = 0`
(ii) `E = 0, B != 0`
(iii) `E != 0, B = 0`
(iv) `E != 0, B != 0`

Options

A. (i), (ii)
B. (ii), (iv)
C. (ii), (iii)
D. (i), (ii), (iv)

Explanation

To solve the problem, we need to analyze the conditions under which a charged particle can move in a gravity-free space without a change in velocity. This means that the net force acting on the particle must be zero.

### Step-by-Step Solution:

1. **Understanding the Forces on a Charged Particle**:
- A charged particle experiences forces due to electric fields (E) and magnetic fields (B). The force due to an electric field is given by \( F_E = qE \) and the force due to a magnetic field is given by \( F_B = q(v \times B) \), where \( q \) is the charge of the particle, \( v \) is its velocity, and \( \times \) denotes the cross product.

2. **Condition for Zero Net Force**:
- For the particle to maintain a constant velocity, the net force must be zero:
\[ F_{net} = F_E + F_B = 0 \]
- This implies that the forces due to the electric and magnetic fields must balance each other out.

3. **Analyzing Each Condition**:
- **Condition (i)**: \( E = 0, B = 0 \)
- If both fields are zero, then there are no forces acting on the particle. This condition is possible.

- **Condition (ii)**: \( E = 0, B \neq 0 \)
- If the electric field is zero and there is a magnetic field, the magnetic force will be zero because \( F_B = q(v \times B) \) will also be zero if \( v = 0 \) or if \( v \) is parallel to \( B \). This condition is possible.

- **Condition (iii)**: \( E \neq 0, B = 0 \)
- If there is an electric field present, there will be a force acting on the particle (\( F_E = qE \)), which will cause it to accelerate. This condition is not possible.

- **Condition (iv)**: \( E \neq 0, B \neq 0 \)
- If both fields are present, the electric force will act in one direction and the magnetic force can act in a perpendicular direction. If they are equal in magnitude and opposite in direction, the net force can be zero. This condition is possible.

4. **Conclusion**:
- The possible conditions where a charged particle can move without changing its velocity in gravity-free space are:
- Condition (i): \( E = 0, B = 0 \)
- Condition (ii): \( E = 0, B \neq 0 \)
- Condition (iv): \( E \neq 0, B \neq 0 \)
- Therefore, the correct answer is that conditions (i), (ii), and (iv) are possible.

### Final Answer:
The possible conditions are (i), (ii), and (iv).