Which of the following statements is correct ?

Options

A. A charged particle can be accelerated by a magnetic field
B. A charged particle cannot be accelerated by a magnetic field
C. The speed of a charged particle can be increased by a uniform magnetic field
D. The speed of a charged particle can be increased by a nonuniform magnetic field

Explanation

To determine which statement is correct regarding the behavior of charged particles in magnetic fields, we can analyze each statement step by step.

### Step-by-Step Solution:

1. **Understanding the Magnetic Force on a Charged Particle**:
- The magnetic force \( F \) on a charged particle moving with velocity \( v \) in a magnetic field \( B \) is given by the equation:
\[ F = q(v \times B) \]
where \( q \) is the charge of the particle. This force is always perpendicular to both the velocity of the particle and the magnetic field.

2. **Effect of Magnetic Force on Kinetic Energy**:
- Since the magnetic force is perpendicular to the velocity, it does not do any work on the charged particle. The work done \( W \) is given by:
\[ W = F \cdot d = Fd \cos(\theta) \]
where \( \theta \) is the angle between the force and displacement. Here, \( \theta = 90^\circ \) (since the force is perpendicular), thus:
\[ W = 0 \]
- Since the work done is zero, the kinetic energy of the particle does not change.

3. **Conclusion on Speed**:
- Because the kinetic energy remains constant, the speed of the charged particle does not change in a uniform magnetic field. However, the direction of the particle's velocity can change due to the magnetic force acting on it.

4. **Analyzing the Statements**:
- **Statement A**: A charged particle can be accelerated by a magnetic field.
- This statement is true because the magnetic field can change the direction of the velocity, which constitutes acceleration.
- **Statement B**: A charged particle cannot be accelerated by a magnetic field.
- This statement is false.
- **Statement C**: The speed of a charged particle cannot be increased by a uniform magnetic field.
- This statement is true; the speed remains constant in a uniform magnetic field.
- **Statement D**: Speed of a charged particle can be increased by a non-uniform magnetic field.
- This statement is misleading; while a non-uniform magnetic field can exert a varying force, it does not directly increase speed in the same way as an electric field would.

5. **Final Answer**:
- The correct statement is **A**: A charged particle can be accelerated by a magnetic field.