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

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    Cyclotron Physics
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Homework Help Overview

The discussion revolves around calculating the energy required for protons to orbit the Earth using a cyclotron that utilizes the Earth's magnetic field. The problem involves understanding the relationship between magnetic forces, centripetal forces, and energy in the context of particle motion in a magnetic field.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the equations related to centripetal force and magnetic force, questioning the units of energy and whether the calculations align with the expected answer. There is also a focus on the potential difference required for protons to maintain their orbit.

Discussion Status

Participants are actively engaging with the problem, raising questions about unit consistency and the assumptions made in the calculations. Some guidance is offered regarding the need to consider gravitational forces in the context of centripetal acceleration, indicating a productive exploration of the topic.

Contextual Notes

There is mention of a sample test from a teacher that lacks unit clarity, leading to confusion among participants regarding the expected format of the answer. Additionally, the absence of the Earth's mass in the original question is noted as a potential oversight.

cheez
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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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"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?
 
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?
 
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. :(
 
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.
 
You probably also have to take into account the role of gravitational force in providing centripetal acceleration apart from magnetic force field.
 
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.
 

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