Monday, March 20, 2017

electromagnetism - Field of moving charge / Lorentz; Liénard-Wiechert


First question here. I'm really confused at the moment. An electron moves at constant velocity, no acceleration


Wikipedia says here Lorentz: $$\mathbf E=\frac{q}{4\pi\epsilon_0}\frac{1-v^2/c^2}{1-v^2\sin^\theta/c^2}\frac{\hat{\mathbf r}}{r^2},$$ which yields something like this:


enter image description here




Whereas here, Wikipedia says this and this, $$ \frac{E'_y}{E'_x} = \frac{E_y}{E_x\sqrt{1-v^2/c^2}} = \frac{y'}{x'}, $$ which yields something like this:



enter image description here


Which one is correct? If you could explain me exactly the reason why one of them is correct, I give you a big imaginary hug.


Last question: In none of those fields is there any radiated energy, since there is no acceleration, correct?




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