A charged particle enters a magnetic field at an angle of `90^(@)`with the magnetic field. The path of the particle will be a/an

Options

A. Helix
B. Ellipse
C. Circle
D. Straight line

Answer

To solve the question about the path of a charged particle entering a magnetic field at an angle of \(90^\circ\) with the magnetic field, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Situation**:
- A charged particle (with charge \(q\)) is moving with a velocity \(v\) and enters a magnetic field \(B\) at an angle of \(90^\circ\).

2. **Magnetic Force on the Charged Particle**:
- The magnetic force \(F\) acting on the charged particle can be calculated using the formula:
\[ F = q(v \times B) \]
- Since the angle between the velocity vector \(v\) and the magnetic field vector \(B\) is \(90^\circ\), the sine of the angle is 1, and the force simplifies to:
\[ F = qvB \]

3. **Direction of the Force**:
- The direction of the magnetic force is given by the right-hand rule. If you point your thumb in the direction of the velocity \(v\) and your fingers in the direction of the magnetic field \(B\), your palm will face in the direction of the force \(F\).

4. **Nature of the Motion**:
- Since the magnetic force is always perpendicular to the velocity of the charged particle, it does not do any work on the particle. This means the speed of the particle remains constant, but its direction changes.
- The particle will experience a centripetal force due to the magnetic field, causing it to move in a circular path.

5. **Conclusion**:
- Therefore, when a charged particle enters a magnetic field at an angle of \(90^\circ\), it will move in a circular path.

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

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