A charged particle is moving with constant velocity in a region, then in which of the following possibility of E & B in that region, is this possible.
(a) `E=0, B=0`
(b) `E=0, Bne0`
(c) `Ene0, B=0
(d) `Ene0, Bne0`

Options

A. a, b, d
B. c, d
C. only c
D. only b

Answer

To solve the problem, we need to analyze the conditions under which a charged particle can move with a constant velocity in the presence of electric (E) and magnetic (B) fields.

### Step-by-Step Solution:

1. **Understanding Constant Velocity**:
A charged particle moving with constant velocity implies that the net force acting on it is zero. According to Newton's first law, if the net force is zero, the particle will continue to move at a constant velocity.

2. **Forces Acting on the Charged Particle**:
The forces acting on a charged particle in an electric field (E) and a magnetic field (B) are given by:
- Electric Force: \( F_E = qE \)
- Magnetic Force: \( F_B = q(v \times B) \)
Here, \( q \) is the charge of the particle, \( v \) is its velocity, and \( \times \) denotes the cross product.

3. **Condition for Zero Net Force**:
For the particle to move with constant velocity, the sum of the electric and magnetic forces must be zero:
\[ F_E + F_B = 0 \]
This means:
\[ qE + q(v \times B) = 0 \]
Simplifying, we have:
\[ E + (v \times B) = 0 \]
This indicates that the electric force can be balanced by the magnetic force.

4. **Analyzing Each Option**:
- **Option (a): \( E = 0, B = 0 \)**:
If both fields are zero, there are no forces acting on the particle. Thus, it can move with constant velocity. **This option is possible.**

- **Option (b): \( E = 0, B \neq 0 \)**:
If the electric field is zero, the magnetic force will depend on the velocity and the magnetic field. If the particle moves parallel to the magnetic field, the magnetic force will be zero. Therefore, it can move with constant velocity. **This option is possible.**

- **Option (c): \( E \neq 0, B = 0 \)**:
If the electric field is non-zero and the magnetic field is zero, the electric force will act on the particle, causing it to accelerate unless there is some other force acting to counter it. Hence, it cannot maintain constant velocity. **This option is not possible.**

- **Option (d): \( E \neq 0, B \neq 0 \)**:
In this case, the electric force can be balanced by the magnetic force if the particle moves at a specific angle to the magnetic field. For example, if the electric field and magnetic field are perpendicular, the forces can cancel each other out, allowing the particle to maintain constant velocity. **This option is possible.**

5. **Conclusion**:
The options that allow a charged particle to move with constant velocity are:
- (a) \( E = 0, B = 0 \)
- (b) \( E = 0, B \neq 0 \)
- (d) \( E \neq 0, B \neq 0 \)

### Final Answer:
The correct options are (a), (b), and (d).