$
\newcommand{\bl}[1]{\boldsymbol{#1}} 
\newcommand{\e}{\bl=}
\newcommand{\p}{\bl+}
\newcommand{\m}{\bl-}
\newcommand{\mb}[1]{\mathbf {#1}}
\newcommand{\mr}[1]{\mathrm {#1}}
\newcommand{\gr}{\bl>}
\newcommand{\les}{\bl<}
\newcommand{\plr}[1]{\left(#1\right)}
\newcommand{\Vlr}[1]{\left\Vert#1\right\Vert}
\newcommand{\vp}{\vphantom{\dfrac{a}{b}}}
\newcommand{\hp}[1]{\hphantom{#1}} 
\newcommand{\x}{\bl\times}
\newcommand{\tl}[1]{\tag{#1}\label{#1}}
$

The relativistic equations for the electromagnetic field of a uniformly moving electric charge $\:q\:$ (see Figure-01) are :

\begin{align}
\mb E\plr{\mb x,t} & \e \dfrac{q}{4\pi\epsilon_0\vp}\dfrac{\plr{1\!\m\!\beta^2}}{\plr{1\!\m\!\beta^2\sin^2\!\phi}^{3/2}\vp}\dfrac{\mb r}{\:\:\Vlr{\mb r}^3},\quad \beta\e\dfrac{\upsilon}{c}
\tl{01a}\\
\mb B\plr{\mb x,t} & \e \dfrac{\mu_0 q}{\hp{\epsilon} 4\pi\hp{_0}\vp}\dfrac{\plr{1\!\m\!\beta^2}}{\plr{1\!\m\!\beta^2\sin^2\!\phi}^{3/2}\vp}\dfrac{\bl\upsilon\x\mb r}{\:\:\Vlr{\mb r}^3},\quad \mb B\e\dfrac{1}{c^2}\plr{\bl\upsilon\x\mb E}\vphantom{\dfrac{a}{\dfrac{}{}b}}
\tl{01b}
\end{align}

The "Correction Coefficient" of the electric field (modified Coulomb field) is
\begin{equation}
\mr{CC}  \e \dfrac{\plr{1\!\m\!\beta^2}}{\plr{1\!\m\!\beta^2\sin^2\!\phi}^{3/2}\vp}
\tl{02}
\end{equation}

So,
\begin{equation}
\mr{CC} \e \left.
\begin{cases}
\gamma^{\m 2}\!\!\!\!\!\!& \les 1 \quad \texttt{in Case 1 :  } \mb r\,\bl \| \,\bl\upsilon \bl\implies \phi\e 0\\
\:\:\:\gamma & \gr 1 \quad \texttt{in Case 2 :  } \mb r\bl \bot \bl\upsilon \bl\implies \phi\e \pi/2\\
\end{cases}
\right\}
\tl{03}
\end{equation}




[![enter image description here][1]][1]


  [1]: https://i.sstatic.net/X0gqK.png