A charged particle having charge q, is moving at right angles to a magnetic field. The quantity which is varying for it is-

Options

A. its kinetic energy
B. its speed
C. its angular velocity
D. its path of motion

Answer

To solve the problem, we need to analyze the motion of a charged particle moving at right angles to a magnetic field. Let's break down the solution step by step.

### Step-by-Step Solution:

1. **Understanding the Situation**:
- A charged particle with charge \( q \) is moving in a magnetic field \( B \) at right angles.
- The motion of the particle will be influenced by the magnetic field, causing it to experience a magnetic force.

2. **Direction of Motion**:
- The charged particle moves with a velocity \( v \) in a direction perpendicular to the magnetic field \( B \).
- According to the right-hand rule, the force acting on the charged particle will be perpendicular to both the velocity and the magnetic field.

3. **Nature of Motion**:
- The magnetic force will cause the charged particle to undergo circular motion. This is because the force acts as a centripetal force, continuously changing the direction of the particle's velocity while keeping its speed constant.

4. **Analyzing Quantities**:
- **Velocity**: The magnitude of the velocity remains constant, but the direction changes continuously, resulting in a change in velocity vector.
- **Speed**: Since speed is the magnitude of velocity, it remains constant throughout the motion.
- **Kinetic Energy**: The kinetic energy \( KE \) of the particle is given by the formula \( KE = \frac{1}{2} mv^2 \). Since \( v \) is constant, the kinetic energy also remains constant.
- **Angular Velocity**: The angular velocity \( \omega \) is defined as \( \omega = \frac{v}{r} \), where \( r \) is the radius of the circular path. Since both \( v \) and \( r \) are constant, \( \omega \) remains constant.

5. **Conclusion**:
- The only quantity that varies is the **path of the motion**. The particle is moving in a circular path, which is continuously changing as it moves.

### Final Answer:
The quantity which is varying for the charged particle is the **path of its motion**.

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