Understanding 4-Momenta Proton Qs: Current Density and Frequency Relationships

[physicsforumsfan]

Hey all,

I have a three part question:

Homework Statement

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

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

Homework Statement

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 traveling 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?

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

Homework Statement

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

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

 

[physicsforumsfan]

Hi,

no reply?

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