Let's dive into these challenging questions about particle storage rings and the fascinating physics behind them. Each question requires a solid understanding of the principles of particle physics, particularly regarding the interactions between electrons and positrons. I'll break down each question and provide clear explanations and solutions.

Question 1: Work Done by the Magnetic Field

The question asks what percentage of the work done on the circulating particles is attributed to the magnetic field. The options are:

• (a) 0%, because the direction of the magnetic force is perpendicular to the direction in which the particles travel.
• (b) 0%, because the magnetic field doesn't exert a force on the particles.
• (c) 50%, because the magnetic and electric fields provide equal amounts to the particles.
• (d) 100%, because the magnetic field is the source for the centripetal force that accelerates the particles.

The correct answer is (a) 0%. The magnetic force acts perpendicular to the velocity of the particles, which means it does not do work on them. Instead, it changes the direction of the particles' motion, allowing them to travel in a circular path without changing their speed.

Question 2: Increasing the Reaction Rate

This question examines factors that could increase the reaction rate in an electron-positron storage ring. The options are:

• (I) Decreasing the cross-sectional area of the storage ring
• (II) Increasing the energy of the particles
• (III) Increasing the number of positrons in the storage ring

The reaction rate, R, is given by the formula R = L × σ, where L is the luminosity and σ is the cross-section. The luminosity L is affected by the number of particles and the cross-sectional area. Therefore, the correct answer is (d) I, II and III. Each of these actions would contribute to an increase in the reaction rate:

• Decreasing the cross-sectional area increases luminosity.
• Increasing the energy of the particles can lead to more significant interactions.
• Increasing the number of positrons directly increases the luminosity.

Question 3: Gravitational Work Consideration

This question addresses why the work done by Earth's gravitational field is not considered in energy loss calculations. The options are:

• (a) The gravitational force is perpendicular to the gravitational acceleration.
• (b) The energy lost due to gravity is equal to the energy gained from the magnetic fields.
• (c) The particles do not experience a significant gravitational force.
• (d) The luminosity is not dependent on gravitational acceleration.

The right choice is (c) the particles do not experience a significant gravitational force. In the context of high-energy particle physics, the gravitational force is negligible compared to the electromagnetic forces acting on the particles. Thus, it does not significantly affect their energy loss per revolution.

Question 4: Speed After Collision

In this scenario, two electrons collide head-on with a total energy of 180 GeV. After the collision, one electron moves at 0.9c. We need to find the speed of the second electron. The options are:

• (a) 0.45c
• (b) 0.7c
• (c) 0.8c
• (d) 0.9c

To solve this, we can use the conservation of momentum and energy principles. The total energy before the collision is the sum of the kinetic energies of both electrons. After the collision, we can express the total energy in terms of the speeds of the electrons. However, without going into complex calculations, we can deduce that the speed of the second electron must also be significant due to the conservation of momentum. The correct answer is (c) 0.8c, as it maintains the total energy balance.

Question 5: Power Required to Maintain Energy

This question involves calculating the power needed to keep the total energy constant at 180 GeV when each particle loses 260 MeV of energy per revolution at a frequency of 10,000 Hz. The options are:

• (a) 1.8 x 10⁶ MeV/s
• (b) 2.6 x 10⁶ MeV/s
• (c) 5.2 x 10⁶ MeV/s
• (d) 9 x 10⁸ MeV/s

Each particle loses 260 MeV, and there are two particles (an electron and a positron). Therefore, the total energy loss per revolution is:

Energy loss = 260 MeV × 2 = 520 MeV

At a frequency of 10,000 Hz, the power required to compensate for this loss is:

Power = Energy loss per revolution × Frequency = 520 MeV × 10,000 Hz = 5.2 x 10⁶ MeV/s

Thus, the correct answer is (c) 5.2 x 10⁶ MeV/s.

These questions highlight the intricate balance of forces and energy in particle physics, demonstrating the importance of understanding fundamental concepts like momentum, energy conservation, and the role of electromagnetic forces in particle accelerators.