A charged particle is at rest in the region where magnetic field and electric field are parallel. The particle will move in a

Options

A. Straight line
B. Circle
C. Ellipse
D. None of these

Answer

To solve the problem of a charged particle at rest in a region where the magnetic field and electric field are parallel, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Initial Conditions**:
- The charged particle is at rest, which means its initial velocity \( V = 0 \).

2. **Understand the Forces Acting on the Particle**:
- The magnetic force \( F_M \) on a charged particle is given by the formula:
\[ F_M = Q V B \sin \theta \]
where \( Q \) is the charge of the particle, \( V \) is its velocity, \( B \) is the magnetic field strength, and \( \theta \) is the angle between the velocity vector and the magnetic field vector.

3. **Evaluate the Magnetic Force**:
- Since the particle is at rest, \( V = 0 \). Substituting this into the magnetic force equation gives:
\[ F_M = Q \cdot 0 \cdot B \cdot \sin \theta = 0 \]
- Therefore, the magnetic force acting on the particle is zero.

4. **Evaluate the Electric Force**:
- The electric force \( F_E \) on the charged particle is given by:
\[ F_E = Q E \]
where \( E \) is the electric field strength.
- This force acts in the direction of the electric field if the charge \( Q \) is positive, and in the opposite direction if \( Q \) is negative.

5. **Determine the Net Force**:
- Since the magnetic force is zero, the only force acting on the particle is the electric force \( F_E \).
- The net force experienced by the charged particle will be due to the electric field only.

6. **Direction of Motion**:
- As a result of the electric force, the charged particle will begin to move in the direction of the electric field (if \( Q \) is positive) or opposite to the electric field (if \( Q \) is negative).
- This motion will be in a straight line either towards the direction of the electric field or away from it.

### Conclusion:
The charged particle will move in a straight line either towards the right or towards the left, depending on the sign of its charge.