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 physical principles at play. This will help us understand the interactions between the light, the ball, and the walls in this setup.

Visualizing the Setup

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

• Wall A: This is the metal wall, positioned on one side of the rectangle.
• Wall B: One of the crown glass walls.
• Wall C: Another crown glass wall.
• Wall D: The last crown glass wall.

Inside this rectangle, we have a ball made of metal Y, which is positioned at a distance "d" from wall A. The distance "d" is much smaller than the length "l" of wall A, indicating that the ball is quite close to this wall.

Light Beams and Their Interaction

From the slits S1 and S2, high-frequency and high-intensity light beams are directed towards the ball. These beams are capable of passing through the crown glass walls (B, C, and D) but not wall A, which is made of metal. The critical point here is that the frequency of the incident light is greater than the threshold frequency for metal Y, meaning that the light has enough energy to potentially cause photoelectric effects on the ball.

Initial Conditions and Charge Dynamics

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

Charge Density = (Q / 4πε₀) * (1/l²)

where "Q" is the total charge on wall A, and "ε₀" is the permittivity of free space. This positive charge creates an electric field that influences the ball's behavior, especially since the ball is made of metal Y.

Behavior of the Ball

When the light beams hit the ball, several things can happen:

• If the light is intense enough, it may cause the ball to gain energy, potentially leading to an increase in its kinetic energy.
• Since the ball is light and the walls are perfectly elastic, any collision with the walls will not result in energy loss, but rather a change in direction.

Implications of the Setup

Given that the floor is frictionless and made of insulating material, the ball will not experience any resistance as it moves. The perfectly elastic nature of the walls means that the ball will rebound off the walls without losing speed. The initial charge on wall A could also induce a charge on the ball, depending on its proximity and the nature of the interaction with the light beams.

Final Thoughts

After the light beams are switched off, the ball will continue to move until it interacts with one of the walls. The impulse from the wall will be just enough to bring the ball to rest, as stated in your scenario. This setup illustrates key concepts in physics, including the behavior of charged objects, the effects of light on materials, and the principles of elastic collisions.

In summary, this arrangement provides a fascinating exploration of how light, charge, and motion interact in a controlled environment. Each element plays a crucial role in determining the outcome of the ball's motion and its interactions with the walls.