Science > Physics > Relativistic electromagnetic equations, gamma not required
| Topic: |
Science > Physics |
| User: |
"srp" |
| Date: |
27 Jul 2005 11:51:11 PM |
| Object: |
Relativistic electromagnetic equations, gamma not required |
Field definitions for individual photons, involving only one variable, the
energy absolute
wavelength
Lambda = (c h)/(Energy in joules)
E = (pi e)/(eps_0 labda^2 alpha^3)
B = (pi mu_0 e c)/(lamba^2 alpha^3)
Where
e = unit charge
c= speed of light
h=Planck's contant
lamba = wavelength of photon considered
alpha = fine structure constant
c=E/B
---------------------------------------------------------------------------------
Field definitions for moving massive particles
Example test particle being the electron, the massive particle's wavelength
used will be Lambda_C (Compton's wavelength)
E = [(pi e) (lambda_C^2+lambda^2) sqrt(4 lambda lambda_C + lambda_C^2)]
/[(eps_0 alpha^3) (lambda_C^2 lambda^2) (2 lambda + lambda_C)]
B = [(pi mu_0 e c) (lambda_C^2 + lambda^2)]/(alpha^3 lambda^2 lambda_C^2)
Calculation of relativistic velocity of test particle
v=E/B
Exact same velocity curve as the traditional SR equation.
All equations extrapolated from Maxwell's 4th equation (Ampere's law
generalized)
also showing the direct link with the Lorentz force equation.
Simplified relativistic velocity equation using only the absolute
wavelengths of
massive particle and carrying energy
v=c sqrt(1 - 1/(1 + (lambda_C/(2 lambda))^2))
Same velocity curve as the traditional SR equation
Have fun retro-deriving them
André Michaud
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