A particle enters uniform constant magnetic field region with is initial velocity parallel to the field direction. Which of the following statements about its velocity is correct ?(neglect the effects of other fields )

Options

A. There is change in both magnitude and direction
B. There is no change
C. There is change only in magnitude
D. There is change only in direction

Answer

To solve the problem, we need to analyze the motion of a charged particle entering a uniform magnetic field with its initial velocity parallel to the field direction.

### Step-by-Step Solution:

1. **Understanding the Magnetic Force**:
The magnetic force acting on a charged particle moving in a magnetic field is given by the Lorentz force equation:
\[ \mathbf{F} = q(\mathbf{v} \times \mathbf{B}) \]
where \( q \) is the charge of the particle, \( \mathbf{v} \) is the velocity vector, and \( \mathbf{B} \) is the magnetic field vector.

2. **Analyzing the Direction of Velocity and Magnetic Field**:
In this case, the initial velocity \( \mathbf{v} \) is parallel to the magnetic field \( \mathbf{B} \). This means that the angle \( \theta \) between \( \mathbf{v} \) and \( \mathbf{B} \) is 0 degrees.

3. **Calculating the Cross Product**:
The cross product \( \mathbf{v} \times \mathbf{B} \) can be calculated using the formula:
\[ |\mathbf{v} \times \mathbf{B}| = |\mathbf{v}| |\mathbf{B}| \sin(\theta) \]
Since \( \theta = 0 \) degrees, we have:
\[ \sin(0) = 0 \]
Therefore, the magnetic force \( \mathbf{F} \) becomes:
\[ \mathbf{F} = q(\mathbf{v} \times \mathbf{B}) = q \cdot 0 = 0 \]

4. **Conclusion on the Motion of the Particle**:
Since the magnetic force is zero, there is no acceleration acting on the particle. According to Newton's first law, if no net force acts on an object, it will continue to move with a constant velocity. Therefore, both the magnitude and direction of the velocity remain unchanged.

5. **Final Answer**:
The correct statement about the velocity of the particle is that there is **no change in velocity**.