# Cyclotron - relationship between velocity and radius

• smart_worker
In summary: AA5mU9Tbut if it is due to radius = velocity/ψ where ψ is the angular frequency,then on increasing velocity kinetic energy increases resulting in increase in ψ,so increase in velocity would be compensated by increase in ψ so radius remain constant resulting in a circular pathso why is the radius not a constant as it keeps increasing uniformly?
smart_worker
cyclotron -- relationship between velocity and radius

in a cyclotron the radius of the path of electron increases.but how if the velocity of the electron is accelerated its kinetic energy should only increase but why is it's radius increasing despite the fact that it's moving to the dee with same polarity?
there is no relation between radius(scalar) and velocity(vector)

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smart_worker said:
in a cyclotron the radius of the path of electron increases.but how if the velocity of the electron is accelerated its kinetic energy should only increase but why is it's radius increasing despite the fact that it's moving to the dee with same polarity?
there is no relation between radius(scalar) and velocity(vector)

Your question is not very clear. Can you please try re-phrasing it to make your question more clear? Perhaps you can refer to the equations on this introductory page to show us what you are confused about:

http://en.wikipedia.org/wiki/Cyclotron

berkeman said:

the radius of the electron is increasing every time its accelerates towards the dee.few websites says its due to the velocity.
my question how can the velocity cause such increment.

is it due to radius = velocity/ψ where ψ is the angular frequency?

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smart_worker said:
the radius of the electron is increasing every time its accelerates towards the dee. wiki page says its due to the velocity.
my question how can the velocity cause such increment.

is it due to radius = velocity/ψ where ψ is the angular frequency?

Where does the wiki page say that? (the part of your quote that I've bolded)

berkeman said:
Where does the wiki page say that? (the part of your quote that I've bolded)

let me correct myself it is not the wiki page stating that i found that in this link

but if it is due to radius = velocity/ψ where ψ is the angular frequency,

then on increasing velocity kinetic energy increases resulting in increase in ψ,so increase in velocity would be compensated by increase in ψ so radius remain constant resulting in a circular path

so why is the radius not a constant as it keeps increasing uniformly?

## 1. What is a cyclotron?

A cyclotron is a type of particle accelerator that uses a magnetic field to accelerate charged particles, typically protons, to high speeds. It is used in scientific research to study the properties of particles and in medical applications to produce radioisotopes for imaging and treatment.

## 2. How does a cyclotron work?

A cyclotron works by using an alternating electric field to accelerate charged particles towards the center of a circular chamber. As the particles gain speed, they are pushed outward by the magnetic field, causing them to travel in a circular path. This process is repeated until the particles reach the desired energy level.

## 3. What is the relationship between velocity and radius in a cyclotron?

In a cyclotron, the speed of the particles increases as they move towards the outer edge of the chamber due to the magnetic field pushing them outward. The radius of the circular path also increases as the particles gain speed, maintaining a constant ratio between the two. This relationship is known as the "velocity selector" and is crucial for the proper functioning of a cyclotron.

## 4. How are the particles steered in a cyclotron?

The particles in a cyclotron are steered by the magnetic field, which is carefully controlled to keep the particles on a circular path. As the particles gain energy, the magnetic field strength is adjusted to maintain the desired radius and keep the particles on track.

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

Cyclotrons have a wide range of applications in both scientific research and medicine. In research, they are used to study the properties of particles and to create high-energy beams for particle physics experiments. In medicine, they are used to produce radioisotopes for medical imaging and cancer treatment.

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