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\begin{document}

\centerline{\Large\underline{Escritura de ecuaciones}}

\vspace{15mm}

\centerline{\textbf{Ecuaciones de Maxwell:}}

\medskip

\begin{equation}
\Phi = \oint_s \vec E \cdot d\vec S = 
\frac{q_{enc}}{\varepsilon_0} \quad \text{(Ley de Gauss)}
\end{equation}

\begin{equation}
\oint_S \vec B \cdot d\vec S = 0 
\quad \text{(Ley de Gauss para el campo magnético)}
\end{equation}

\begin{equation}
\oint_C \vec{E} \cdot d\vec{l} = 
- \frac{d}{dt}\int_S \vec B \cdot d\vec S 
\quad \text{(Ley de Faraday)}
\end{equation}

\begin{equation}
\oint_C \vec{B} \cdot d\vec{l} = \mu_0 \int_S \vec{j} \cdot d\vec{S} +
 \mu_0 \epsilon_0 \frac{d}{dt} \int_S \vec{E} \cdot d\vec{S} 
\quad \text{(Ley de Ampére)}
\end{equation}

\vspace{15mm}

\centerline{\textbf{Formulación covariante del campo electromagnético:}}

\medskip
\begin{equation}
\mathbf{F} = F_{\mu \nu} = 
\begin{pmatrix} 0 & E_x/c & E_y/c & E_z/c \\ 
-E_x/c & 0 & -B_z & B_y \\ 
-E_y/c & B_z & 0 & -B_x \\ 
-E_z/c & -B_y & B_x & 0 
\end{pmatrix}
\end{equation}

\medskip
\begin{equation}
\ f_{\alpha} = \sum_{\beta} e \ F_{\alpha \beta} \ u^{\beta} \qquad 
\qquad \partial_{\mu} F^{\mu \nu} = 
\mu_0 J^{\nu} \partial_\mu \cdot F^{\mu \nu} = 0
\end{equation}


\end{document}
