When a charged particle moves perpendicular to a magnetic field, then:

Options

A. speed of the particles is changed
B. speed of the particle remains unchanged
C. direction of motion of the particle remains unchanged
D. acceleration of the particle remains unchanged

Answer

To solve the question, "When a charged particle moves perpendicular to a magnetic field, then:", we need to analyze the behavior of the charged particle under the influence of the magnetic field.

### Step-by-Step Solution:

1. **Understanding the Situation**:
- A charged particle (let's say with charge +q) is moving in a direction perpendicular to a uniform magnetic field (B).
- The direction of the magnetic field is represented as going into the page (denoted by a cross).

2. **Applying the Lorentz Force**:
- The force acting on the charged particle due to the magnetic field is given by the Lorentz force formula:
\[ \mathbf{F} = q(\mathbf{v} \times \mathbf{B}) \]
- Here, \( \mathbf{v} \) is the velocity of the charged particle, and \( \mathbf{B} \) is the magnetic field.

3. **Determining the Force Direction**:
- The angle \( \theta \) between the velocity vector and the magnetic field vector is 90 degrees (since they are perpendicular).
- Therefore, the magnitude of the force can be calculated as:
\[ F = qvB \sin(90^\circ) = qvB \]
- The direction of the force can be determined using the right-hand rule, which shows that the force is perpendicular to both the velocity and the magnetic field.

4. **Motion of the Charged Particle**:
- Since the magnetic force is always perpendicular to the velocity, it does not do work on the particle. This means that the speed (the magnitude of the velocity) of the particle remains constant.
- However, the direction of the velocity changes continuously, causing the particle to move in a circular path.

5. **Acceleration of the Particle**:
- The acceleration of the particle is directed towards the center of the circular path (centripetal acceleration). The magnitude of this acceleration is given by:
\[ a = \frac{v^2}{r} \]
- Although the magnitude of the acceleration remains constant (as both speed and radius are constant), the direction of the acceleration changes continuously as the particle moves in a circle.

6. **Conclusion**:
- From the analysis, we can conclude:
- The speed of the particle remains unchanged.
- The direction of motion of the particle changes continuously.
- The acceleration of the particle changes in direction, although its magnitude remains constant.

### Final Answer:
- The correct option is: **Speed of the particle remains unchanged**.