A positively charged particle moving along x-axis with a certain velocity enters a uniform electric field directed along positive y-axis. Its

Options

A. Vertical velocity changes but horizontal velocity remains constant
B. Horizontal velocity changes but vertical velocity remains constant
C. Both vertical and horizontal velocities change
D. Neither vertical nor horizontal velocity changes

Answer

To solve the problem, we need to analyze the motion of a positively charged particle as it enters a uniform electric field. The particle is initially moving along the x-axis, and the electric field is directed along the y-axis. Let's break down the solution step by step.

### Step-by-Step Solution:

1. **Identify the Initial Conditions:**
- The positively charged particle is moving along the x-axis with an initial velocity \( v_x \).
- The electric field \( \mathbf{E} \) is directed along the positive y-axis.

2. **Determine the Force Acting on the Particle:**
- Since the particle has a charge \( Q \), it will experience a force due to the electric field. The force \( \mathbf{F} \) can be calculated using the formula:
\[ \mathbf{F} = Q \mathbf{E} \]
- This force acts in the direction of the electric field, which is the positive y-direction.

3. **Analyze the Motion in the y-Direction:**
- The force acting on the particle in the y-direction will cause it to accelerate. According to Newton's second law, the acceleration \( a_y \) in the y-direction can be expressed as:
\[ a_y = \frac{F}{m} = \frac{Q E}{m} \]
- This means that the vertical velocity \( v_y \) of the particle will change over time due to this acceleration.

4. **Analyze the Motion in the x-Direction:**
- In the x-direction, there is no force acting on the particle (since the electric field is only in the y-direction). Therefore, the acceleration \( a_x \) in the x-direction is:
\[ a_x = 0 \]
- Since there is no acceleration in the x-direction, the horizontal velocity \( v_x \) remains constant.

5. **Conclusion:**
- The vertical velocity of the particle changes due to the acceleration caused by the electric field, while the horizontal velocity remains constant because there is no force acting in that direction.

### Final Answer:
- The vertical velocity changes, but the horizontal velocity remains constant.