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

Options

A. Energy remains constant but momentum 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 problem step by step:

### Step 1: Understanding the Motion of the Charged Particle
When a charged particle enters a uniform magnetic field perpendicularly, it experiences a magnetic force that acts perpendicular to both the velocity of the particle and the magnetic field. This force causes the particle to move in a circular path.

**Hint:** Recall the right-hand rule to determine the direction of the magnetic force acting on the charged particle.

### Step 2: Analyzing Energy
The work done by the magnetic force on the charged particle is zero because the magnetic force is always perpendicular to the direction of motion. Since the work done is zero, the kinetic energy of the particle remains constant throughout its motion in the magnetic field.

**Hint:** Remember that kinetic energy is given by the formula \( KE = \frac{1}{2}mv^2 \), where \( m \) is mass and \( v \) is velocity.

### Step 3: Analyzing Momentum
Momentum is defined as the product of mass and velocity (\( p = mv \)). While the speed (magnitude of velocity) of the particle remains constant, the direction of the velocity changes continuously as the particle moves in a circular path. Therefore, the momentum of the particle changes because it is a vector quantity, and its direction is changing.

**Hint:** Consider how momentum is affected by changes in direction, even if the speed remains constant.

### Step 4: Conclusion
Based on the analysis:
- The energy of the charged particle remains constant.
- The momentum of the charged particle changes due to the change in direction.

Thus, the correct answer to the question is that the energy remains constant while the momentum changes.

**Final Answer:** The correct option is **Option 1: Energy remains constant but momentum changes.**