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 is the initial perpendicular distance between ball, and wall A, and given:(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 walls 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 interactions taking place. This will help us understand the dynamics of the system involving the ball, the walls, and the light beams.

Diagram Overview

Imagine a rectangular slab viewed from above. The walls are labeled as follows:

• A: The metal wall
• B: A crown glass wall
• C: Another crown glass wall
• D: The last crown glass wall

Inside this rectangle, we have a ball made of metal Y, positioned at a distance "d" from wall A, where "d" is much smaller than the length "l" of wall A. The ball's diameter is equal to the length of wall A, meaning it fits snugly within the rectangle.

Light Beams and Their Interaction

Two slits, S1 and S2, are located outside the rectangle. High-frequency, high-intensity light beams are emitted from these slits, passing through the transparent walls B, C, and D, and striking the ball. Importantly, these beams never hit wall A, which is crucial for understanding the charge dynamics at play.

Charge Dynamics

Initially, wall A is positively charged with a specific charge density given by the formula:

Charge Density = (Q / 4πε₀) >> (l²)

Here, "Q" represents the total charge on wall A, and "ε₀" is the permittivity of free space. This positive charge creates an electric field that influences the behavior of the ball.

Behavior of the Ball

When the light beams strike the ball, they impart energy to it. Since the frequency of the incident beams exceeds the threshold frequency for metal Y, we can expect photoelectric effects to occur. This means that the ball may gain kinetic energy from the absorbed light, potentially leading to an increase in its motion.

Elastic Collisions and Impulse

Given that all walls and the ball are perfectly elastic, any interaction between the ball and the walls will conserve momentum and energy. When the ball collides with wall B, C, or D, it will bounce back without losing energy. However, the problem states that the impulse on the ball due to the wall obstructing its motion is just enough to bring it to rest. This implies that the ball will momentarily stop upon hitting one of the walls, but it will not lose any energy in the process.

Final Thoughts

After the light beams are switched off, the ball's behavior will depend on the interactions it had with the walls and the energy it absorbed from the light. The frictionless floor ensures that no additional forces act on the ball, allowing us to focus solely on the elastic collisions and the effects of the electric field from wall A. This setup provides a fascinating glimpse into the interplay between light, charge, and motion in a controlled environment.