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 (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. We have a rectangular slab with walls labeled A, B, C, and D, and a ball made of metal Y positioned inside. The walls B, C, and D are made of crown glass, while wall A is a metal wall. Light beams are emitted from slits S1 and S2, striking the ball without ever hitting wall A. This setup leads to interesting interactions between light, charge, and motion.

Understanding the Setup

First, let's clarify the components of the arrangement:

• Rectangular Slab: This is the container for the ball, with walls A, B, C, and D.
• Ball: Made of metal Y, it is lightweight and has a diameter equal to the length of wall A.
• Walls: Wall A is metallic and positively charged, while walls B, C, and D are transparent crown glass.
• Slits S1 and S2: These are openings through which high-frequency, high-intensity light beams enter the slab.

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 the photons in the light beams have enough energy to cause the photoelectric effect in the ball. When the light hits the ball, it can impart energy to the electrons in metal Y, potentially causing them to be ejected from the surface of the ball.

Charge Dynamics

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

Charge on wall A = (Q/4πε₀) * l²

where Q is the total charge and l is the length of wall A. The positive charge on wall A creates an electric field that influences the ball. Since the ball is made of metal Y, it can also become charged due to the photoelectric effect when illuminated by the light beams.

Ball Dynamics and Motion

Given that the floor is frictionless and made of an insulating material, the ball can move freely within the slab. The initial distance between the ball and wall A is denoted as "d," which is much smaller than the length of wall A (d << l). This proximity to the positively charged wall A means that the ball will experience an attractive force due to the electric field created by wall A.

Elastic Collisions and Impulse

Since all walls and the ball are perfectly elastic, any collision between the ball and the walls will conserve kinetic energy and momentum. When the ball is illuminated and potentially charged, it may experience a repulsive force from wall A if it gains a negative charge due to the ejected electrons. However, the problem states that the impulse on the ball due to the wall is just enough to bring it to rest, indicating that the ball will not collide with wall A but rather come to a halt due to the forces acting on it.

Conclusion of the Dynamics

In summary, the arrangement you've described involves complex interactions between light, charge, and motion. The ball, influenced by the electric field of wall A and the energy from the light beams, experiences forces that dictate its motion within the slab. The perfectly elastic nature of the walls and the ball ensures that energy is conserved, while the insulating floor allows for unimpeded movement. This scenario beautifully illustrates principles of electromagnetism, optics, and mechanics in a cohesive manner.