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)Ball's 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 physics involved. Imagine a rectangular slab viewed from above, with walls labeled A, B, C, and D. The ball is placed inside this rectangle, and we have two slits, S1 and S2, positioned outside the rectangle. The walls B, C, and D are made of crown glass, while wall A is constructed from a metal, referred to as metal X. The ball itself is made of another metal, metal Y.

Understanding the Setup

The arrangement is designed to explore the interaction between light and charged objects. Here’s a breakdown of the components:

• Walls B, C, D: These are transparent and allow light to pass through.
• Wall A: This is a metal wall that is positively charged, creating an electric field around it.
• Ball: Made of metal Y, it is lightweight and has a diameter equal to the length of wall A.
• Slits S1 and S2: These are the sources of high-frequency, high-intensity light beams that will interact with the ball.

Light Interaction with the Ball

The light beams emitted from slits S1 and S2 have a frequency greater than the threshold frequency for metal Y. This means that when these beams strike the ball, they can cause the ball to emit electrons due to the photoelectric effect. The ball, being lightweight and elastic, will respond to this energy transfer.

Charge Dynamics and Motion

Initially, wall A has a positive charge described by the equation (Q/4πε₀) >> (l²), where Q is the charge on wall A and l is the length of the rectangle. The ball is positioned at a distance d from wall A, where d is much smaller than l (d << l). This proximity to the positively charged wall means that the ball will experience an attractive force due to the electric field created by wall A.

Behavior of the Ball

When the light beams are switched on, they strike the ball, potentially causing it to gain energy and emit electrons. However, since the ball is also influenced by the electric field from wall A, it will experience a net force towards wall A. The ball's motion is further complicated by the fact that the floor is frictionless, allowing it to move freely without resistance.

Elastic Collisions and Resting State

Given that all walls and the ball are perfectly elastic, when the ball interacts with the walls, 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 the ball to rest. This implies that the ball will eventually stop moving after colliding with the walls, despite the energy it initially received from the light beams.

Final Thoughts

In summary, the arrangement you've described is a fascinating interplay of light, charge, and motion. The ball, influenced by both the electric field from wall A and the energy from the light beams, will initially move but will ultimately come to rest due to the elastic nature of the collisions with the walls. This scenario beautifully illustrates principles of electromagnetism and the behavior of charged particles in electric fields.