a charged particle moves in a gravity free space without change in velocity. Which of the following is/are possible?

Options

A. `E=0 and B!=0`
B. `E!=0 and B=0`
C. `E!=0 and B!=0`
D. `E=0, B=0`

Explanation

To solve the problem of a charged particle moving in a gravity-free space without a change in velocity, we need to analyze the conditions under which this can occur. We will consider the effects of electric fields (E) and magnetic fields (B) on the motion of the charged particle.

### Step-by-Step Solution:

1. **Understanding the Motion of Charged Particles:**
A charged particle experiences forces when placed in electric and magnetic fields. 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 \( B \) is the magnetic field.

2. **Case 1: \( E = 0 \) and \( B \neq 0 \)**
- If there is no electric field and a magnetic field is present, the charged particle will experience a magnetic force that acts perpendicular to its velocity. This results in circular motion, where the speed remains constant, but the direction changes.
- **Conclusion:** This case is possible.

3. **Case 2: \( E \neq 0 \) and \( B = 0 \)**
- If there is an electric field present and no magnetic field, the particle will experience a force \( F_E = qE \). This force will cause the particle to accelerate, changing its velocity.
- **Conclusion:** This case is not possible.

4. **Case 3: \( E \neq 0 \) and \( B \neq 0 \)**
- In this scenario, both electric and magnetic forces are acting on the particle. The forces can balance each other if \( qE = qvB \), leading to a constant velocity. This means the particle can move at a constant speed in a straight line if the forces are equal and opposite.
- **Conclusion:** This case is possible.

5. **Case 4: \( E = 0 \) and \( B = 0 \)**
- If both fields are absent, there are no forces acting on the particle. Thus, it will continue to move at a constant velocity (Newton's first law).
- **Conclusion:** This case is possible.

### Summary of Results:
- **Possible Cases:**
- Case 1: \( E = 0 \), \( B \neq 0 \) (Circular motion, constant speed)
- Case 3: \( E \neq 0 \), \( B \neq 0 \) (Balanced forces, constant speed)
- Case 4: \( E = 0 \), \( B = 0 \) (No forces, constant speed)

- **Not Possible:**
- Case 2: \( E \neq 0 \), \( B = 0 \) (Acceleration, changing velocity)

### Final Answer:
The possible scenarios for a charged particle moving in a gravity-free space without a change in velocity are Case 1, Case 3, and Case 4.

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