Question

The work done by the magnetic field on a charged particle in motion in a cyclotron is zero. How, then, can a cyclotron be used as a particle accelerator, and what essential feature of the particle's motion makes it possible?

Short answer

Short Answer: In a cyclotron, the magnetic field keeps the charged particles moving in circular paths, without changing their speed or kinetic energy. This is because the magnetic force is always perpendicular to the direction of motion and does no work on the particles. The acceleration is provided by the alternating electric field, which does work on the charged particles as they pass through the gap between the two semi-circular plates called the "D's." Thus, the essential feature of the particle's motion in a cyclotron that enables its function as a particle accelerator is the combination of the constant magnetic field for confinement and the alternating electric field for acceleration.

Step-by-step solution

Understand basic cyclotron operation

A cyclotron is a type of particle accelerator that uses a combination of alternating electric fields and a constant magnetic field to accelerate charged particles. The charged particles are forced to move in circular paths by the magnetic field, and they are accelerated by the electric field as they pass through a gap between two semi-circular plates, called the "D's".

Understand the role of the magnetic field

The magnetic field in a cyclotron plays the role of keeping the charged particles moving in circular paths. When a charged particle moves in a magnetic field, it experiences a magnetic force that is perpendicular to both the particle's velocity and the magnetic field. This force causes the particle to move in a circular path with a constant speed, as the force acts as a centripetal force. It's important to note that the magnetic force does no work on the particles since the force is always perpendicular to the direction of motion. This means that the magnetic field cannot change the speed or kinetic energy of the particle, only its direction.

Understand the role of the electric field

The electric field in a cyclotron is responsible for accelerating the charged particles. As the particle passes through the gap between the D's, it experiences an electric force that is parallel to the direction of motion. This force does work on the particles and increases their kinetic energy, causing them to accelerate. The electric field switches direction every half cycle, ensuring that the charged particles are accelerated each time they pass through the gap.

Explain the essential feature of the particle's motion

The essential feature of the particle's motion in a cyclotron that makes it possible for the cyclotron to be used as an accelerator is the fact that the magnetic field keeps the charged particles confined in a circular path while the electric field provides the acceleration. This combination of fields allows for charged particles to gain kinetic energy and increase their speed despite the magnetic field not doing any work on them directly. The acceleration happens due to the alternating electric field and the confinement occurs due to the constant magnetic field, making the cyclotron an effective particle accelerator.