A charged particle moves through a magnetic field perpendicular to its direction. Then

Options

A. The momentum changes but the kinetic energy is constant
B. Both momentum and kinetic energy of the particle are not constant
C. Both momentum and kinetic energy of the particle are constant
D. Kinetic energy changes but the momentum is constant

Explanation

To solve the question regarding the behavior of a charged particle moving through a magnetic field perpendicular to its direction, we will analyze the effects on momentum and kinetic energy step by step.

### Step-by-Step Solution

1. **Understand the Motion of the Charged Particle**:
- When a charged particle moves through a magnetic field that is perpendicular to its velocity, it experiences a magnetic force that acts as a centripetal force. This force causes the particle to move in a circular path.

**Hint**: Remember that the magnetic force acts perpendicular to the velocity of the charged particle, resulting in circular motion.

2. **Identify the Nature of Momentum and Kinetic Energy**:
- Momentum (p) is defined as the product of mass (m) and velocity (v) of the particle:
\[ p = m \cdot v \]
Momentum is a vector quantity, meaning it has both magnitude and direction.
- Kinetic energy (KE) is given by the formula:
\[ KE = \frac{1}{2} m v^2 \]
Kinetic energy is a scalar quantity, meaning it only has magnitude and no direction.

**Hint**: Recall the definitions of momentum and kinetic energy, focusing on their vector and scalar nature.

3. **Analyze the Speed of the Particle**:
- In circular motion, while the direction of the velocity changes, the magnitude (speed) of the velocity remains constant. Since the magnetic field is constant and the force is perpendicular, the speed does not change.

**Hint**: Consider how circular motion affects speed and direction separately.

4. **Evaluate the Kinetic Energy**:
- Since the speed of the particle remains constant and mass is constant, the kinetic energy does not change:
\[ KE = \frac{1}{2} m v^2 \quad \text{(remains constant)} \]

**Hint**: Think about how changes in speed affect kinetic energy.

5. **Evaluate the Momentum**:
- Although the magnitude of the velocity remains constant, the direction of the velocity is continuously changing as the particle moves in a circular path. Therefore, the momentum, which depends on both mass and velocity (a vector), is changing due to the change in direction.
- Thus, the momentum is not constant:
\[ p = m \cdot v \quad \text{(changes due to direction)} \]

**Hint**: Focus on how direction affects vector quantities like momentum.

6. **Conclusion**:
- The final conclusion is that while the kinetic energy of the charged particle remains constant, the momentum changes due to the change in direction of the velocity.
- Therefore, the answer to the question is:
- **Momentum changes, but kinetic energy remains constant.**

### Final Answer
- **Momentum changes, Kinetic Energy is constant.**