When there is a charge moving at a constant speed $\vec{u}$, the induced electric field $\vec{E}$ and magnetic field $\vec{B}$ would be:

$$\vec{E}=\frac{q}{4\pi\epsilon r^2} \frac{1−\beta^2}{\left(1−\beta^2\sin^2\theta\right)^\frac32}\hat{r}\tag{01}\label{01}$$

$$\vec{B}=\frac{\vec{u}\times\vec{E}}{c^2}\tag{02}\label{02}$$

How to derive them?

When there is a charge moving at a constant speed $\vec{u}$, the induced electric field $\vec{E}$ and magnetic field $\vec{B}$ would be:

$$\beta=\frac{u}{c}\tag{01}$$

$$\vec{E}=\frac{q}{4\pi\epsilon r^2} \frac{1−\beta^2}{\left(1−\beta^2\sin^2\theta\right)^\frac32}\hat{r}\tag{02}$$

$$\vec{B}=\frac{\vec{u}\times\vec{E}}{c^2}\tag{03}$$

How to derive them?

When there is a charge moving at a constant speed $\vec{u}$, the induced electric field $\vec{E}$ and magnetic field $\vec{B}$ would be: $\vec{E}=\frac{q}{4π\epsilon r^2} \frac{1−β^2}{(1−β^2sin^2θ)^\frac{3}{2}}\hat{r}$

$\vec{B}=\frac{\vec{u}\times\vec{E}}{C^2}$

How to derive them?

When there is a charge moving at a constant speed $\vec{u}$, the induced electric field $\vec{E}$ and magnetic field $\vec{B}$ would be:

$$\vec{E}=\frac{q}{4\pi\epsilon r^2} \frac{1−\beta^2}{\left(1−\beta^2\sin^2\theta\right)^\frac32}\hat{r}\tag{01}\label{01}$$

$$\vec{B}=\frac{\vec{u}\times\vec{E}}{c^2}\tag{02}\label{02}$$

How to derive them?