A charged particle is released from a rest in a region, having steady and uniform electric and magnetic fields . If the two fields are parallel to each other, Then the path of the particle will be :

Options

A. ellipse
B. circle
C. helix
D. straight line

Answer

To solve the problem, we need to analyze the forces acting on a charged particle released from rest in a region with uniform electric and magnetic fields that are parallel to each other.

### Step-by-Step Solution:

1. **Understanding the Initial Conditions**:
- The charged particle is initially at rest, meaning its initial velocity \( v = 0 \).
- The electric field \( \vec{E} \) and magnetic field \( \vec{B} \) are parallel to each other.

**Hint**: Remember that the forces acting on the charged particle depend on its initial state (rest in this case).

2. **Identifying the Forces**:
- When a charged particle is placed in an electric field, it experiences an electric force given by:
\[ \vec{F_E} = q \vec{E} \]
- Since the particle is at rest initially, the magnetic force, which is given by:
\[ \vec{F_B} = q (\vec{v} \times \vec{B}) \]
will be zero because the velocity \( \vec{v} = 0 \).

**Hint**: Recall that the magnetic force depends on the velocity of the charged particle.

3. **Motion Due to Electric Force**:
- The electric force \( \vec{F_E} \) will cause the particle to accelerate in the direction of the electric field.
- As the particle starts moving under the influence of the electric force, it gains velocity.

**Hint**: The direction of the electric force is crucial as it determines the direction of motion of the particle.

4. **Analyzing the Motion**:
- As the particle accelerates, its velocity becomes non-zero. However, since the magnetic field is parallel to the electric field, the angle \( \theta \) between the velocity vector and the magnetic field remains zero degrees.
- The magnetic force can be expressed as:
\[ \vec{F_B} = qvB \sin(\theta) \]
Since \( \theta = 0 \), \( \sin(0) = 0 \), thus \( \vec{F_B} = 0 \).

**Hint**: The relationship between the velocity vector and the magnetic field is key to understanding the absence of magnetic force.

5. **Conclusion on the Path of the Particle**:
- Since the magnetic force is zero, the only force acting on the charged particle is the electric force.
- Therefore, the charged particle will continue to move in a straight line in the direction of the electric field.

**Hint**: The absence of a magnetic force means the particle does not experience any deviation from its path.

### Final Answer:
The path of the charged particle will be a **straight line**.