# Do the electric field and magnetic field derived from the Lienard-Wiechert potentials satisfy Gauss's law?

I've already got the electric fields and magnetic fields derived from the Lienard-Wiechert potentials:

$${\bf E}=\frac{q}{4\pi\epsilon_0}\frac{R}{(\bf R\cdot u)^3}[(c^2-v^2){\bf u}+\bf R\times(u\times a)]$$

$${\bf B}=\frac{\bf R}{cR}\times\bf E$$

where $${\bf R=r-r'}$$ and $${\bf u}=\frac{c\bf R}{R}-\bf v$$.

I wonder if they satisfy Maxwell's equations, I've tried to derive Gauss's law, but in vain. So do they? Or is there something wrong in my derivation?

• The first term of $\mathbf{E}$ is not a vector. – SuperCiocia Jun 28 '20 at 3:31
• Thank you! I've rectified it. – Soluty Jun 28 '20 at 12:15
• Isn't $u$ a vector? So isn't the first term of $E$ a vector? – J Thomas Jun 29 '20 at 17:32