A charged particle enters a uniform magnetic field perpendicular to it. The magnetic field

Options

A. Increases the speed of the particle
B. Decreases the kinetic energy of the particle.
C. Changes the direction of motion of the particle
D. Both 1 and 3

Answer

To solve the problem of a charged particle entering a uniform magnetic field perpendicular to its motion, we can follow these steps:

### Step-by-Step Solution

1. **Understanding the Scenario**:
- A charged particle (let's say with charge \( Q \)) is moving with a velocity \( \vec{V} \) and enters a uniform magnetic field \( \vec{B} \) that is perpendicular to the velocity of the particle.

2. **Applying the Lorentz Force**:
- The force acting on the charged particle due to the magnetic field is given by the Lorentz force equation:
\[ \vec{F} = Q (\vec{V} \times \vec{B}) \]
- Since the magnetic field is perpendicular to the velocity, the angle between \( \vec{V} \) and \( \vec{B} \) is \( 90^\circ \).

3. **Direction of the Force**:
- The direction of the force \( \vec{F} \) can be determined using the right-hand rule. If you point your fingers in the direction of \( \vec{V} \) and curl them towards \( \vec{B} \), your thumb will point in the direction of the force \( \vec{F} \).

4. **Effect on the Motion of the Particle**:
- The force \( \vec{F} \) is always perpendicular to the velocity \( \vec{V} \). This means that while the speed of the particle remains constant, the direction of the velocity changes.
- As a result, the particle will move in a circular path due to the centripetal nature of the force acting on it.

5. **Work Done and Kinetic Energy**:
- Since the force is perpendicular to the displacement of the particle, the work done by the magnetic force is zero:
\[ W = \vec{F} \cdot \vec{d} = 0 \]
- Because the work done is zero, there is no change in the kinetic energy of the particle. The speed of the particle remains constant.

6. **Conclusion**:
- The correct answer to the question is that the magnetic field changes the direction of motion of the particle, but it does not change its speed or kinetic energy. Therefore, the correct option is:
- **Option 3: Changes the direction of motion of the particle.**