Moving Charges And MagnetismClass 12 Physics Case Study Questions

A hospital is installing a new medical cyclotron to produce radioisotopes for Positron Emission Tomography (PET) scans. This device accelerates protons to very high energies. The core of the cyclotron consists of two hollow, D-shaped metal containers called 'dees', placed in a vacuum chamber. A strong, uniform magnetic field is applied perpendicular to the plane of the dees, while a high-frequency alternating electric field is applied across the gap between them.

A proton injected near the center is accelerated by the electric field and then forced into a circular path by the magnetic field. Each time it crosses the gap, the electric field reverses, accelerating it further and increasing the radius of its path. This process continues, with the proton spiraling outwards at increasing speeds until it reaches the desired energy and is extracted to strike a target, producing the needed radioisotopes.

An apprentice electrician was using a magnetic compass to find the north direction while installing wiring in a new building. He noticed that whenever he was near a specific wall cavity where a thick bundle of wires was running, his compass needle would deflect wildly, pointing away from the true north. The deflection was most significant when the main power to the floor was on and a large industrial heater was running. He observed that if he moved the compass further away from the wall, the deflection decreased, and the needle would gradually realign with the Earth's magnetic north. Reversing the connections on the heater also changed the direction of the compass deflection.

In a physics laboratory, a student sets up an experiment to demonstrate the magnetic force on a current-carrying conductor. A straight copper wire of length $1.5 \text{ m}$ and mass $200 \text{ g}$ is placed horizontally. A uniform horizontal magnetic field is applied perpendicular to the wire. The student connects the wire to a variable power supply and slowly increases the current. At a specific current of $2.0 \text{ A}$, the student observes that the wire is suspended in mid-air, perfectly balancing the force of gravity.

The setup is designed to be in a region where the Earth's magnetic field is negligible. The student notes that the direction of the current and the magnetic field are crucial for achieving levitation.