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4-Momenta Proton Qs.

  1. Nov 6, 2013 #1
    Hey all,

    I have a three part question:
    1. The problem statement, all variables and given/known data

    If A^(3)=(Ax,Ay,Az) is the three-vector potential, J^(3)=(Jx,Jy,Jz) is the three-vector current density, [itex]\varphi[/itex] is the scalar potential and p is the charge density, then the four-current density J is given by:

    3. The attempt at a solution

    I have read through literature and believe the answer is:

    c=speed of light

    J=(cp Jx Jy Jz) -> I am confused because can this answer be written transposed in a matrix and still be correct or is this answer only valid in the form:

    J=(cp,Jx,Jy,Jz)?

    Part 2

    1. The problem statement, all variables and given/known data

    A photon is produced in frame S with 4-momentum P=(E/c,p,0,0) and frequency f , where hf=pc=E, p is the magnitude of the 3-momentum and E is the energy. Frame S' is travelling at speed v in the direction of the positive x axis of frame S. What is the relationship between the 4-momenta P and P in the two frames?

    3. The attempt at a solution

    Using invariance of 4-momentum, Squaring P' will yield:

    P'^2= (γP)^2 where γ is Lorentz factor 1/√1-v^2/c^2

    Thus sqrt answer is:

    P' = P/√(1-v^2/c^2)

    Is this correct?

    Part 3

    1. The problem statement, all variables and given/known data

    In the previous question, what is the relationship between the frequencies f and f' of the photon in the two frames?

    3. The attempt at a solution

    Taking inverse of f', you get

    f' = 1/(γf) = f*√(1-v^2/c^2) or is it take the square and then sqrt it to give:

    f'= f/√(1-v^2/c^2)

    That's it,

    Thanks
     
  2. jcsd
  3. Nov 6, 2013 #2
    Hi,

    no reply?

    Help?
     
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