A particle moves in a region having a uniform magnetic field and a parallel, uniform electric field. At some instant, the velocity of the particle is perpendicular to the field direction. The path of the particle will be

Options

A. a straight line
B. a circle
C. a helix with uniform pitch
D. a helix with nonuniform pitch

Answer

To solve the problem, we need to analyze the motion of a charged particle in the presence of both a magnetic field and an electric field. The key points to consider are the effects of each field on the particle's motion.

### Step-by-Step Solution:

1. **Understanding the Fields**:
- We have a uniform magnetic field (B) and a uniform electric field (E) that are parallel to each other.
- The velocity (v) of the charged particle is perpendicular to the direction of both fields at a certain instant.

2. **Effect of the Magnetic Field**:
- When a charged particle moves in a magnetic field, it experiences a magnetic force given by the equation:
\[ F_B = q(v \times B) \]
- Since the velocity is perpendicular to the magnetic field, the magnetic force will act perpendicular to both the velocity and the magnetic field, causing the particle to move in a circular path.

3. **Effect of the Electric Field**:
- The electric field exerts a force on the charged particle given by:
\[ F_E = qE \]
- This force acts in the direction of the electric field and causes the particle to accelerate.

4. **Combining the Effects**:
- The magnetic force causes circular motion, while the electric force causes linear acceleration in the direction of the electric field.
- As a result, the particle will not only move in a circle due to the magnetic field but will also gain a component of motion along the direction of the electric field.

5. **Resulting Path**:
- The combination of circular motion from the magnetic field and linear motion from the electric field results in a helical path.
- However, since the electric field causes a constant acceleration, the pitch of the helix will not be uniform; it will vary as the particle accelerates.

6. **Conclusion**:
- Therefore, the path of the particle will be a helix with non-uniform pitch.

### Final Answer:
The path of the particle will be a helix with non-uniform pitch.