The path executed by a charged particle whose motion is perpendicular to magnetic field is

Options

A. A straight line
B. An ellipse
C. A circle
D. A helix

Answer

To determine the path executed by a charged particle whose motion is perpendicular to a magnetic field, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Situation**:
- A charged particle (let's say with charge +q) is moving in a magnetic field (B) that is perpendicular to its velocity (v).
- The angle between the velocity vector and the magnetic field vector is 90 degrees.

2. **Apply the Lorentz Force Law**:
- The force acting on the charged particle due to the magnetic field is given by the equation:
\[ F = q(v \times B) \]
- Since the angle between v and B is 90 degrees, the magnitude of the force can be simplified to:
\[ F = qvB \sin(90^\circ) = qvB \]

3. **Direction of the Force**:
- The direction of the force can be determined using the right-hand rule. Point your fingers in the direction of the velocity (v) and curl them towards the magnetic field (B). Your thumb will point in the direction of the force (F).

4. **Nature of the Motion**:
- The magnetic force acts perpendicular to the velocity of the charged particle. This means that the force does not do work on the particle (as work is force in the direction of displacement), and it only changes the direction of the velocity, not its magnitude.
- Since the force is always directed towards the center of the circular path, the particle will undergo uniform circular motion.

5. **Conclusion**:
- Therefore, the path executed by the charged particle is a **circle**.

### Final Answer:
The path executed by a charged particle whose motion is perpendicular to the magnetic field is a **circle**.

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