When a charged particle moves in an elecltric or a magnetic field, its speed is `v` and acceleration is `a`

Options

A. In a magnetic field, v is constant if the particle moves in a circular path, and variable if it moves in a helical path
B. In a magnetic field, v is always constant, a may or may not be zero
C. In an electric field, v can never remain constant
D. In a uniform electric field, a must be constant in magnitude and direction

Explanation

To solve the question regarding the behavior of a charged particle moving in electric or magnetic fields, we will analyze the statements provided in the question step by step.

### Step 1: Understanding Motion in a Magnetic Field
When a charged particle moves in a magnetic field, it experiences a magnetic force that is perpendicular to its velocity. This causes the particle to move in a circular or helical path depending on the angle of its velocity with respect to the magnetic field.

- **Circular Path**: If the charged particle moves perpendicular to the magnetic field, it will follow a circular path with constant speed. The acceleration is centripetal and directed towards the center of the circle.
- **Helical Path**: If the charged particle moves at an angle to the magnetic field, it will follow a helical path. The speed remains constant, but the direction of the velocity changes continuously.

**Conclusion**: The first statement is incorrect because both paths (circular and helical) involve constant speed.

### Step 2: Behavior of Magnetic Field and Acceleration
In a magnetic field, the magnetic field strength (B) is typically constant, while the acceleration (A) can vary depending on the motion of the charged particle.

- The magnetic field (B) does not change as it is a property of the region in space.
- The acceleration may vary, especially if the particle's path is not uniform.

**Conclusion**: The second statement is incorrect as it implies that acceleration must be zero, which is not necessarily true.

### Step 3: Motion in an Electric Field
In an electric field, a charged particle experiences a force that causes it to accelerate. The speed of the particle can change as it moves through the electric field.

- The acceleration is determined by the electric field and is constant in magnitude and direction if the electric field is uniform.
- However, the speed of the particle is not constant; it increases as it moves along the field.

**Conclusion**: The third statement is correct; in an electric field, the speed of the particle can never remain constant.

### Step 4: Uniform Electric Field and Acceleration
In a uniform electric field, the force acting on the charged particle is constant, leading to constant acceleration.

- The acceleration is constant in both magnitude and direction as long as the electric field is uniform.

**Conclusion**: The fourth statement is correct; in a uniform electric field, acceleration must be constant in both magnitude and direction.

### Final Summary of Statements:
1. **First Statement**: Incorrect
2. **Second Statement**: Incorrect
3. **Third Statement**: Correct
4. **Fourth Statement**: Correct