$ \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} as shown in Figure-02.
