If a charged particle enters perpendicular in the uniform magnetic field then

Options

A. Energy remains constant but moment changes
B. Energy and momentum both remains constant
C. Momentum remains constant but energy changes
D. Neither energy nor momentum remains constant

Answer

To solve the question regarding the behavior of a charged particle entering a uniform magnetic field perpendicularly, we can break down the solution step by step.

### Step-by-Step Solution:

1. **Understanding the Situation**:
- A charged particle (like an electron or proton) is entering a uniform magnetic field at a right angle (90 degrees) to the direction of the magnetic field lines.

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

3. **Direction of the Force**:
- Since the particle enters the magnetic field perpendicularly, the angle between the velocity vector and the magnetic field vector is 90 degrees. Thus, the magnetic force will be at a right angle to the velocity of the particle.

4. **Work Done by the Magnetic Field**:
- The work done by a force is given by the equation:
\[ W = \vec{F} \cdot \vec{d} \]
where \( \vec{d} \) is the displacement. Since the magnetic force is always perpendicular to the displacement of the charged particle, the work done by the magnetic field is zero:
\[ W = 0 \]

5. **Kinetic Energy**:
- Since the work done is zero, the kinetic energy of the charged particle remains constant. The equation for kinetic energy is:
\[ KE = \frac{1}{2} mv^2 \]
where \( m \) is the mass and \( v \) is the speed of the particle. Since the speed does not change, the kinetic energy remains constant.

6. **Momentum Change**:
- Although the kinetic energy remains constant, the direction of the velocity changes due to the magnetic force acting on the particle. Momentum \( \vec{p} \) is given by:
\[ \vec{p} = m\vec{v} \]
Since the direction of \( \vec{v} \) changes, the momentum of the particle also changes even though its magnitude (speed) remains constant.

7. **Conclusion**:
- Therefore, when a charged particle enters a uniform magnetic field perpendicularly, the energy remains constant while the momentum changes due to the change in direction of the velocity.

### Final Answer:
- Energy remains constant, but momentum changes.