# Cyclotron Motion: Does Charge Require Energy to Move?

• Kolahal Bhattacharya
In summary, a particle in a cyclotron motion requires energy provided by the magnetic field to start, and the energy remains constant as long as radiation is neglected and the B field does no work on the charge. To set the charge into motion, it must be accelerated through means other than the B field, such as passing through accelerating segments or injecting it into the B field after being accelerated in an electric field.
Kolahal Bhattacharya
We know in a cyclotron motion, qvB=mv^2/R
Can you please tell me if the charge requires energy as it moves...
It is obvious that when it starts it requires energy provided by only the magnetic field. As it starts, it has constant velocity...no dissipation.Does it mean its energy remains constant?Then is Lorentz force is conservative?

The B field does no work on a moving charge.
The particle would circle at constant speed and energy if radiation is neglected.

If B field does not do any work,how the charge sets into motion?

Kolahal Bhattacharya said:
If B field does not do any work,how the charge sets into motion?

One must set the charge in motion by some means other than the B field. For example, one can accelerate the charges along a straignt line in an electric field and then "inject" the beam into the B field.

Or, while the charges are circulating in the B field, they can pass through short accelerating segments that produce an electric field. As the particles gain momentum, one increases the B field in step so as to keep the radius of the orbit constant. A modern large ring-accelerator like the ones at CERN and Fermilab has alternating accelerating and bending segments.

## 1. What is cyclotron motion?

Cyclotron motion is the circular motion of a charged particle in a uniform magnetic field. It occurs when the magnetic force on the charged particle balances the centripetal force, causing the particle to move in a circular path.

## 2. How does a cyclotron work?

A cyclotron works by accelerating charged particles in a circular path using a combination of an electric field and a magnetic field. The particles are injected into the center of the cyclotron and are accelerated by the electric field as they move towards the edge. The magnetic field then bends their path, causing them to circulate and gain energy with each revolution.

## 3. Does charge require energy to move in a cyclotron?

Yes, charge does require energy to move in a cyclotron. The electric field in a cyclotron is used to accelerate the charged particles, and as the particles gain energy, the radius of their circular path increases. Therefore, the energy input is necessary to maintain the circular motion of the particles.

## 4. What factors affect the energy required for cyclotron motion?

The energy required for cyclotron motion is affected by the strength of the magnetic field, the charge of the particles, and the radius of the circular path. A stronger magnetic field or a larger radius will require more energy to maintain the circular motion.

## 5. What are the applications of cyclotron motion?

Cyclotron motion has many applications in fields such as particle physics, medical imaging, and nuclear medicine. It is used to accelerate charged particles for research and medical purposes, such as creating medical isotopes for diagnostic imaging and cancer treatment.

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