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Hello,
A charge q is at rest in frame O. In O' with velocity βc in x direction, at t'=0 the charge is at the origine O' and produce an electric field E' at position r'=(x',y',z') :
E'=γ*q*(x',y',z')/(4πεo*γ²(x'²+y'²+z'²)3/2)
If θ is the angle between r' and x, show that:
E'=q*r'/(4πεo*γ²*r'²(1-βsin²θ)*r')
I'm blocking at this step :
E'=q*r'/(4πεo*γ²*(x'²+(y'²+z'²)/γ²)^3/2)
sinθ=y'/r' but I can't find a way to find the asked formula, I think that there's something that I'm missing but don't know what.
Thanks
Homework Statement
A charge q is at rest in frame O. In O' with velocity βc in x direction, at t'=0 the charge is at the origine O' and produce an electric field E' at position r'=(x',y',z') :
E'=γ*q*(x',y',z')/(4πεo*γ²(x'²+y'²+z'²)3/2)
If θ is the angle between r' and x, show that:
E'=q*r'/(4πεo*γ²*r'²(1-βsin²θ)*r')
Homework Equations
The Attempt at a Solution
I'm blocking at this step :
E'=q*r'/(4πεo*γ²*(x'²+(y'²+z'²)/γ²)^3/2)
sinθ=y'/r' but I can't find a way to find the asked formula, I think that there's something that I'm missing but don't know what.
Thanks