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. Stright line
B. Circle
C. Ellipse
D. None of these

Answer

To solve the problem, we need to analyze the motion of a charged particle that is initially at rest in a region where both the electric field (E) and magnetic field (B) are parallel. Let's break down the solution step by step:

### Step 1: Understanding the Forces Acting on the Particle
A charged particle in an electric and magnetic field experiences a force known as the Lorentz force, which is given by the equation:
\[ \mathbf{F} = q\mathbf{E} + q(\mathbf{v} \times \mathbf{B}) \]
where:
- \( \mathbf{F} \) is the total force,
- \( q \) is the charge of the particle,
- \( \mathbf{E} \) is the electric field,
- \( \mathbf{v} \) is the velocity of the particle,
- \( \mathbf{B} \) is the magnetic field.

### Step 2: Initial Conditions
Since the particle is at rest initially, its velocity \( \mathbf{v} = 0 \). Therefore, the magnetic force component \( q(\mathbf{v} \times \mathbf{B}) \) becomes zero:
\[ \mathbf{F}_{\text{magnetic}} = q(0 \times \mathbf{B}) = 0 \]

### Step 3: Force Due to Electric Field
The only force acting on the particle at this moment is due to the electric field:
\[ \mathbf{F}_{\text{electric}} = q\mathbf{E} \]
This force will cause the particle to accelerate.

### Step 4: Acceleration and Motion
As the particle experiences a force \( q\mathbf{E} \), it will gain velocity in the direction of the electric field. Since the magnetic field is parallel to the electric field, the angle \( \theta \) between the velocity vector and the magnetic field vector remains either 0° or 180°, resulting in:
\[ \mathbf{v} \times \mathbf{B} = 0 \]
Thus, the magnetic force remains zero throughout the motion.

### Step 5: Conclusion about the Motion
Since the particle starts moving due to the electric field and the magnetic field does not exert any force on it (as established), the particle will move in a straight line in the direction of the electric field.

### Final Answer
The charged particle will move in a straight line.

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