Calculating Proton Energy for a Large Cyclotron Using Earth's Magnetic Fields

In summary, the conversation discusses the calculation of energy in volts for protons to orbit the Earth at a certain height using a large, cheap cyclotron and the Earth's magnetic fields. The final answer is 1.56 x 10^13 V, but there is some confusion about the units and the role of gravitational force in the calculation.
  • #1
cheez
26
0
You plan to build a large, cheap cyclotron using the Earth's magnetic fields(1x10^-4 T) and orbiting just above the Earth's atmosphere (radius 5.7 x10 ^6 m) What energy, in volts, should protons be given to just circle the earth? q= 1.6 x10^-19 C, m= 1.67x10^-27
The answer is 1.56 x 10^13
I can't get the answer.

Fm = F centripetal Force
qvB = mv^2/r
v= rqB/m

Calculate energy

KE = 1/2 mv^2
I put in v = rqB/m

KE= 1/2 (rqB)^2/m

I plug in all the #, but still can't the answer

please help, thanks so much!
 
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  • #2
"The answer is 1.56 x 10^13
I can't get the answer."

The answer is not 10^13V (not an energy) or 10^13eV (zowies!). What is the answer again?
 
  • #3
What are the units of the given solution?

What are the units of your answer?

Are they the same?

What happens if you make them the same?
 
  • #4
The anwer doesn't have unit. (This is the sample test from my teacher, he doesn't type units for answer.) But in the question, it said volts. The unit I got is Newton x Seconds/ kg. Actually, I don't know how to make it into volts. I don't even know if it's the right method. :(
 
  • #5
Some misunstanding is here. Sorry about that. The answer my teacher gave is 1.56 x 10^13 V. I can't get the same answer as my teacher from the calculation above.
 
  • #6
You probably also have to take into account the role of gravitational force in providing centripetal acceleration apart from magnetic force field.
 
  • #7
arunbg said:
You probably also have to take into account the role of gravitational force in providing centripetal acceleration apart from magnetic force field.


Cheez's question doesn't include the mass of the earth, so it seems it should be disregarded. From my perspective it seem the question is asking:

Through what potential difference should the protons be accelerated through for the protons to just orbit the Earth (at the same height)?

Which would lead to an answer in Volts.
 

What is a cyclotron and how does it work?

A cyclotron is a type of particle accelerator that uses a strong magnetic field to accelerate charged particles in a spiral motion. The particles are then directed into a target, where they can be used for various experiments or applications.

What are the main components of a cyclotron?

The main components of a cyclotron include a vacuum chamber, a strong magnet, an ion source, and a target. The vacuum chamber provides a low-pressure environment for the particles to travel through, while the magnet creates a strong magnetic field to guide the particles. The ion source produces the particles, and the target is where the particles are directed for experiments or applications.

What is the purpose of a cyclotron in scientific research?

A cyclotron is used in scientific research to study the properties and behavior of particles, as well as to produce and study new particles. It can also be used in medical applications, such as in cancer treatment, where the accelerated particles are directed to target and destroy cancer cells.

How is energy conserved in a cyclotron?

In a cyclotron, the particles are accelerated by an alternating electric field, which increases their kinetic energy. The magnetic field then keeps the particles in a circular path, ensuring that the energy is conserved. As the particles move faster and faster, the magnetic field is adjusted to keep the particles on the same path while increasing their energy.

What are some challenges in designing and operating a cyclotron?

Some challenges in designing and operating a cyclotron include maintaining a stable magnetic field, controlling the beam of particles, and minimizing energy losses due to collisions with the chamber walls. Additionally, the cost of building and maintaining a cyclotron can be a challenge, as it requires specialized equipment and expertise.

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