# Max speed of proton in cyclotron

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In summary, the solution to this problem is that the proton will escape from the magnetic field if the B-field is only there for a portion of the protons path.
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Homework Statement
Relevant Equations
For this problem,

The solution is,

However, I don't understand why they say just before the proton escapes? Are they assuming that the B-field is only at a portion of region which means that only half or so of the circular path is within the B-field so only half of the path have a magnetic centripetal force?

If the B-field is only there for a portion of the protons path, how do they know that max speed is reached?

Many thanks!

The say "just before the proton escapes" to give you indirectly a numerical value. Which of the two values in the statement of the problem do you think that is?

member 731016
kuruman said:
The say "just before the proton escapes" to give you indirectly a numerical value. Which of the two values in the statement of the problem do you think that is?
The max speed is ##5.17 \times 10^7 \frac {m}{s}##?

Callumnc1 said:
The max speed is ##5.17 \times 10^7 \frac {m}{s}##?
I said the "in statement of the problem", not in the solution that follows it.

member 731016
kuruman said:
I said the "in statement of the problem", not in the solution that follows it.
Oh I see - thanks @kuruman!

It means max speed of proton over region of radius 1.20 m with B-field strength of 0.450 T.

EDIT: However, I still don't see how the proton would escape since theoretically it should continue moving in the circle of radius 1.20 m as the magnetic force provides the centripetal force. What would cause it to leave the B-field?

Protons in a cyclotron are accelerated. This means that the radius of the orbit increases until they escape. Look it up here to see how it's done.

member 731016
kuruman said:
Protons in a cyclotron are accelerated. This means that the radius of the orbit increases until they escape. Look it up here to see how it's done.
Thanks @kuruman , will do!

Callumnc1 said:
Thanks @kuruman , will do!
Ah so understanding the cyclotron principle I see now that you don't have to calculate the electric force on the protons going from each dee as that info can be gauged from the magnetic field strength and cyclon frequency that does not depend on radius.

## What is the maximum speed a proton can reach in a cyclotron?

The maximum speed a proton can reach in a cyclotron is limited by relativistic effects and typically approaches a significant fraction of the speed of light, but not exceeding it. In practical terms, this speed can be around 30% to 50% of the speed of light, depending on the cyclotron's design and energy limits.

## Why can't a proton reach the speed of light in a cyclotron?

A proton cannot reach the speed of light in a cyclotron due to the principles of relativity. As the proton's speed increases, its mass effectively increases, requiring exponentially more energy to continue accelerating. Thus, it can get very close but never actually reach the speed of light.

## What factors determine the maximum speed of a proton in a cyclotron?

The maximum speed of a proton in a cyclotron is determined by several factors, including the magnetic field strength, the radius of the cyclotron, the energy supplied to the proton, and the relativistic effects that come into play as the proton's speed increases.

## How is the speed of a proton measured in a cyclotron?

The speed of a proton in a cyclotron is typically measured using detectors that track its position and momentum, as well as through calculations based on the energy imparted to the proton and the magnetic field strength. These measurements can be quite precise, allowing scientists to determine the proton's speed at various stages of acceleration.

## What advancements have been made to increase the maximum speed of protons in cyclotrons?

Advancements to increase the maximum speed of protons in cyclotrons include improvements in magnetic field strength, better vacuum systems to reduce energy loss, more efficient RF (radio frequency) acceleration systems, and the development of superconducting magnets. These advancements help to push the limits of proton speed while managing the effects of relativity.

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