First, draw a rectangular slab.

Mark the walls A,B,C,D.(not the vertices)

Put a ball inside.

Draw 2 slits S1,S2 outside the rectangle.

Follow the following directions carefully henceforth:

1)The diagram drawn is the top view of an arrangement.

2)Medium pervading empty space is vacuum.

3)Walls B,C,D are crown glass walls.

4)Wall A is made of metal X

5)Ball is made of metal Y

6)From the slits S1,S2, light beams are incident, having very high frequency, as well as very high intensity. Frequency of incident beams is greater than threshold frequency for metal Y. Light beams are incident in such a manner that they pass through transparent walls and hit the ball. However, the never at any instant of time hit wall A.

7)Initially wall A is +vely charged with

(Q/4-pi-epsilon-nought)>>(l^2)

where Q=charge on wall A, and , l=length of rectangle(wall A is one of the sides representing width of rectangle).

8)d :the initial perpendicular distance between ball, and wall A, and (l>>d)

9)S1,S2 are allowed to emit light beams for a fraction of second only, and then they are switched off.

10)Floor is frictionless, made of insulating material.

11)Balls diameter is equal to length of wall A, and is light.

12)All walls and ball are perfectly elastic.

13)Assume that impulse on ball due to the wall obstructing the balls motion is just enougth to put the ball at rest.

There is no answer given. Just the question itself.

To visualize the scenario you've described, let's break it down step by step, focusing on the arrangement and the physics involved. We have a rectangular slab with walls labeled A, B, C, and D. The ball is placed inside this slab, and light beams are directed towards it through slits S1 and S2. Here's how we can understand the situation in detail.

Visualizing the Setup

Imagine looking down at a rectangular box from above. The walls are positioned as follows:

• Wall A: This is the metal wall, positively charged, and it is one of the shorter sides of the rectangle.
• Walls B, C, D: These are made of crown glass, which is transparent to the light beams.

The ball, made of metal Y, is placed inside the box, away from wall A, at a distance "d." The diameter of the ball is equal to the length of wall A, which means it fits snugly within the rectangle.

Light Beams and Their Interaction

The light beams emitted from slits S1 and S2 are of very high frequency and intensity, surpassing the threshold frequency for metal Y. This means that the light can cause the ball to become excited, potentially leading to the emission of electrons from the surface of the ball due to the photoelectric effect.

Charge Dynamics

Initially, wall A has a positive charge described by the formula:

Charge on wall A = (Q/4πε₀) * l²

Here, "Q" represents the total charge on wall A, and "l" is the length of the rectangle. The positive charge on wall A creates an electric field that influences the ball's behavior, especially since the ball is made of metal Y.

Ball Dynamics and Elastic Collisions

As the light beams hit the ball, they impart energy to it. Given that the floor is frictionless and the walls are perfectly elastic, the ball will respond to the forces acting on it. The impulse from the walls, when the ball collides with them, is just enough to bring the ball to rest momentarily. This means that the ball will bounce back without losing energy due to the elastic nature of the collisions.

Understanding the Impulse and Motion

Since the ball is light and the walls are rigid, when the ball collides with any wall (B, C, or D), it will experience a change in momentum. The impulse delivered by the wall will be equal to the change in momentum of the ball. If the ball is at rest after the collision, it means that the impulse was sufficient to counteract its motion effectively.

Conclusion of the Dynamics

After the light beams are switched off, the ball will remain at rest due to the lack of external forces acting on it, aside from the electric field created by wall A. The interactions between the light beams, the ball, and the walls illustrate fundamental principles of physics, including the photoelectric effect, elastic collisions, and the behavior of charged objects in an electric field.

This scenario encapsulates a fascinating interplay of light, charge, and motion, demonstrating key concepts in both classical mechanics and electromagnetism. If you have any further questions or need clarification on any specific point, feel free to ask!