Solving Cyclotron Movement Problem with 500V and 0.790B

In summary, a 61.0 cm diameter cyclotron with a 500 V oscillating potential difference between the dees and a magnetic field strength of 0.790 ? is being discussed. The question at hand is how many revolutions a proton would make before leaving the cyclotron. Relevant equations include v/r=Bq/m and Ke=1/2mv^2. The poster mentions being stumped on the problem and having calculated the maximum speed and kinetic energy, but not knowing how to determine the number of revolutions from there. They ask for hints and mention the electron leaving the cyclotron and reaching escape speed. Michel asks for a description of how the device works and how the electron reaches escape speed.
  • #1
24
0

Homework Statement



A 61.0 cm diameter cyclotron uses a 500 V oscillating potential difference between the dees. The magnetic field strength is 0.790 ?

How many revolutions would a proton make before leaving the cyclotron?

Homework Equations



v/r=Bq/m Ke=1/2mv^2

The Attempt at a Solution



I am completely stumped on this problem, I have calculated the max speed, and therefor max kinetic energy. But cannot figure out how to derive number of revolutions from there.

Any hints would be greatly appreciated.

Thanks
 
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  • #2
Canadian,

Why would the electron leave the cyclotron,
Describe first how this device works.
How does the electron reach the escape speed?

Michel
 
  • #3
for your question. I understand your struggle with this problem. Let's break it down and see if we can come up with a solution together.

First, let's review the basics of a cyclotron. A cyclotron is a type of particle accelerator that uses a combination of electric and magnetic fields to accelerate charged particles, such as protons, to high energies. The particles are injected into the center of the cyclotron and are then accelerated by the electric field between two metal plates called "dees" that have a potential difference between them. As the particles gain speed, they are deflected by a magnetic field, causing them to spiral outward until they reach the outer edge of the cyclotron.

Now, let's apply this knowledge to the given problem. We know the diameter of the cyclotron (61.0 cm) and the strength of the magnetic field (0.790 ?). We also know that the potential difference between the dees is 500 V. Using the equation Ke=1/2mv^2, we can calculate the maximum kinetic energy of the proton as it reaches the outer edge of the cyclotron. However, we also need to consider the magnetic force acting on the proton as it spirals outward. This force is given by F=qvB, where q is the charge of the proton, v is its velocity, and B is the magnetic field strength. This force must be equal to the centripetal force acting on the proton, which is given by F=mv^2/r, where m is the mass of the proton and r is the radius of its circular path.

Putting these equations together, we can set F=qvB=mv^2/r, and solve for v to get v=Br/q. Now we have an expression for the velocity of the proton in terms of the magnetic field strength and the charge of the proton. Substituting this into the equation for kinetic energy, we get Ke=1/2m(Br/q)^2.

We also know that the maximum kinetic energy of the proton is equal to the potential difference between the dees, so we can set Ke=500 V. Solving for r, we get r=qB/500. This tells us the radius of the proton's circular path at the outer edge of the cyclotron.

Now, we can use the circumference formula, C=2πr, to calculate the distance the proton travels in one revolution.
 

1. How does a cyclotron work?

A cyclotron is a type of particle accelerator that uses a combination of electric and magnetic fields to accelerate charged particles to high speeds. These particles are then used for various purposes, such as medical imaging or nuclear research.

2. What is the purpose of solving the cyclotron movement problem?

The purpose of solving the cyclotron movement problem is to determine the trajectory of charged particles as they move through the cyclotron's electric and magnetic fields. This information is crucial for optimizing the design and function of the cyclotron, as well as for predicting the behavior of the particles being accelerated.

3. How is the movement of particles in a cyclotron affected by voltage and magnetic field strength?

The movement of particles in a cyclotron is affected by both the electric field, which is controlled by the voltage, and the magnetic field strength. The electric field causes the particles to accelerate, while the magnetic field causes them to move in a circular path. The strength of these fields determines the speed and trajectory of the particles.

4. How can the cyclotron movement problem be solved with 500V and 0.790B?

The cyclotron movement problem can be solved by using the equations that describe the motion of charged particles in electric and magnetic fields. These equations take into account the values of voltage and magnetic field strength, as well as other factors such as the mass and charge of the particles. By plugging in the values of 500V and 0.790B, the trajectory of the particles can be calculated.

5. What are some applications of solving the cyclotron movement problem?

The solutions to the cyclotron movement problem can be used to optimize the design and function of the cyclotron, ensuring efficient and accurate acceleration of particles. This information is also important for predicting the behavior of particles in other types of particle accelerators, as well as in various scientific and medical applications, such as cancer treatment and nuclear research.

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