In a cyclotron, the time to make it all the way around is Different

In summary, the formula t= gamma * t' can be applied if the path is circular. This formula is important for GPS location, but there is an additional term that depends on the observer's location due to centripetal acceleration. However, there seems to be disagreement about the validity of this formula in relation to gravitational time dilation.
  • #1
physics user1
Can I apply the formula t= gamma * t' if the path is Circular?
 
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  • #2
Why would you want to do that ?
 
  • #3
That formula is important for GPS location. But there is another term, due to the centripetal acceleration, that also depends on the observer's location.
 
  • #4
Meir Achuz said:
That formula is important for GPS location. But there is another term, due to the centripetal acceleration, that also depends on the observer's location.
Are you trying to talk about gravitational time dilation in the context of a centrifugal acceleration field? Sounds like hogwash.
 
  • #5
Cozma Alex said:
Can I apply the formula t= gamma * t' if the path is Circular?
Yes. In special relativity the only thing that matters is the instantaneous speed, and that's constant here.

You can prove it by integrating the interval along the circular path of you want.
 
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1. What is a cyclotron?

A cyclotron is a type of particle accelerator that uses an oscillating electric field to accelerate charged particles.

2. How does a cyclotron work?

In a cyclotron, charged particles are injected into a chamber between two hollow, semicircular electrodes. An alternating electric field is applied, causing the particles to accelerate towards the outer edge of the electrodes. As they gain speed, they are guided by a magnetic field and continue to spiral outward, increasing in speed until they reach the desired energy level.

3. Why does the time to make it all the way around in a cyclotron vary?

The time to make it all the way around in a cyclotron can vary due to a number of factors, including the strength and frequency of the electric field, the mass and charge of the particles being accelerated, and the size and design of the cyclotron.

4. How is the time to make it all the way around in a cyclotron calculated?

The time to make it all the way around in a cyclotron is calculated using the equation T = 2πm/qB, where T is the time, m is the mass of the particle, q is its charge, and B is the strength of the magnetic field.

5. What are some practical applications of cyclotrons?

Cyclotrons are used in a variety of fields, including medicine, nuclear physics, and material science. They are used to produce medical isotopes for diagnostic and therapeutic purposes, to study the structure of atomic nuclei, and to create and study new materials with unique properties.

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