A magnetic field

Options

A. always exerts a force on a charged par ticle
B. never exerts a force on a charged particle
C. exerts a force, if the charged particle is moving along the magnetic field lines
D. exerts a force, if the charged particle is moving across the magnetic field lines

Answer

To solve the question regarding the behavior of a charged particle in a magnetic field, we need to analyze the options provided based on the principles of electromagnetism.

### Step-by-Step Solution:

1. **Understanding the Magnetic Force on a Charged Particle**:
The force \( F \) on a charged particle moving in a magnetic field is given by the formula:
\[ F = Q \cdot V \cdot B \cdot \sin(\theta) \]
where:
- \( F \) is the magnetic force,
- \( Q \) is the charge of the particle,
- \( V \) is the velocity of the particle,
- \( B \) is the magnetic field strength,
- \( \theta \) is the angle between the velocity vector and the magnetic field direction.

2. **Analyzing Each Option**:
- **Option 1**: "A magnetic field always exerts a force on a charged particle."
- This is incorrect because if the charged particle is at rest (\( V = 0 \)) or moving parallel to the magnetic field lines (\( \theta = 0 \) or \( 180^\circ \)), then \( F = 0 \).

- **Option 2**: "A magnetic field never exerts a force on a charged particle."
- This is also incorrect because a magnetic field can exert a force on a charged particle when it is moving at an angle to the magnetic field lines (\( 0 < \theta < 180^\circ \)).

- **Option 3**: "A magnetic field exerts a force on a charged particle if it is moving along the magnetic field lines."
- This is incorrect as well. If the charged particle is moving along the magnetic field lines (\( \theta = 0 \)), the force \( F \) will be zero since \( \sin(0) = 0 \).

- **Option 4**: "A magnetic field exerts a force if the charged particle is moving across the magnetic field."
- This is correct. When the charged particle moves across the magnetic field lines, \( \theta \) is not \( 0 \) or \( 180^\circ \), thus \( \sin(\theta) \) is non-zero, and a force will be exerted on the particle.

3. **Conclusion**:
Based on the analysis of the options, the correct answer is:
**Option 4**: A magnetic field exerts a force if the charged particle is moving across the magnetic field.