A charged particle enters in a magnetic field B with its initial velocity making an angle of 45° with B. The path of the particle will be

Options

A. an ellipse
B. straight line
C. a circle
D. a heilical

Answer

To determine the path of a charged particle entering a magnetic field at an angle, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Information**:
- A charged particle enters a magnetic field \( B \).
- The initial velocity \( V \) makes an angle of \( 45^\circ \) with the magnetic field \( B \).

2. **Resolve the Velocity into Components**:
- The velocity can be resolved into two components:
- **Component parallel to the magnetic field**:
\[ V_{\parallel} = V \sin(45^\circ) = V \cdot \frac{1}{\sqrt{2}} \approx 0.707V \]
- **Component perpendicular to the magnetic field**:
\[ V_{\perpendicular} = V \cos(45^\circ) = V \cdot \frac{1}{\sqrt{2}} \approx 0.707V \]

3. **Analyze the Motion of the Particle**:
- The component of velocity parallel to the magnetic field (\( V_{\parallel} \)) will cause the particle to move in a straight line along the direction of the magnetic field.
- The component of velocity perpendicular to the magnetic field (\( V_{\perpendicular} \)) will cause the particle to undergo circular motion due to the magnetic force acting on it.

4. **Combine the Motions**:
- The combination of the straight-line motion (due to \( V_{\parallel} \)) and the circular motion (due to \( V_{\perpendicular} \)) results in a helical path.
- The particle moves forward in the direction of the magnetic field while simultaneously moving in a circular path due to the perpendicular component of its velocity.

5. **Conclusion**:
- Therefore, the path of the charged particle will be helical.

### Final Answer:
The path of the particle will be **helical**.