# [Physics] Field of moving charge / Lorentz; Liénard-Wiechert

electromagnetismlienard-wiechertspecial-relativity

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:

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:

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?

Both equations (for the instantaneous field of a charge moving with constant velocity $v$) are correct. (Well, maybe the primes should be swapped in the second equation, so that the unprimed frame is that in which the charge is moving.)
The first figure is not an accurate representation of the first equation: as Jan Lalinsky stated, the field lines should be symmetric about $\theta=\pi/2$, the direction perpendicular to the velocity.