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physicsforumsfan
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Hey all,
I have a three part question:
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:
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
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?
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
In the previous question, what is the relationship between the frequencies f and f' of the photon in the two frames?
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
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, [itex]\varphi[/itex] 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