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Radius cyclotron

  1. Aug 25, 2010 #1
    1. The problem statement, all variables and given/known data
    A cyclotron is to accelerate protons to an energy of 5.4 MeV. The superconducting electromagnet of the cyclotron produces a magnetic field of 3.5 T, perpendicular to the proton’s orbits.
    a) When the protons have achieved a kinetic energy of 2.7 MeV, what is the radius of their circular orbit and what is their angular speed?
    b) Repeat part a) when the protons have achieved their final kinetic energy of 5.4 MeV.

    2. Relevant equations
    R=mv/qB
    fc=qB/(2pi*m)


    3. The attempt at a solution
    google calc
    2.7 megaelectron volts = 4.32587645 × 10-13 joules
    mass of a proton 1.67262158 × 10-27 kilograms
    elementary charge = 1.60217646 × 10-19 coulombs
    K=1/2mv2 not totally sure if I can use this -cant see why not either???
    v=2.2743*107
    subbing all values in
    R=0.068m
    not sure what sort of range these are usually in so I can't tell if my answer seems right or not??????

    found fc to be 5.33588*107Hz so w=3.353*108rad/s

    I really just need to know if these values seem right and someone to check my procedure(and answers if your really nice). b is the same so i wont bother wasting time with that.
    thanks for any help
     
  2. jcsd
  3. Aug 25, 2010 #2
    Yeah, that seems right, though I'll admit that I didn't do the numbers myself. I think you should be using w = v/R though.
     
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