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\begin{document}

\begin{center}

\Large{\textsc{Worksheet 2b}: \textbf{Gauss's Theorem}}

\end{center}

\vspace{.5mm}

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%% INFO %%
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\begin{tabular}{rl}
\textsc{SI Leader}:
&
Stephen Iota (\email{siota001@ucr.edu})
\\
\textsc{Course}:
&
Physics 40C (Fall 2018), Dr.~Laura Sales
\\
\textsc{Date}:
&
11 October 2018
\end{tabular}

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\section{Conceptual Questions}

\begin{enumerate}[label=(\alph*)]

\item A metallic sphere of radius $r = 5 \ \mu$m with a total charge of $-12.3$ nC is placed in an electric field $\vec{E}(\vec{r}) = 3.2 \hat{x} + 5.7 \hat{y}  - 7.3 \hat{z}$ N/C. What is the electric field strength inside ($r<R$) the sphere?
\item Is Gauss's Law only valid for symmetric charge distributions?  	

\end{enumerate}

 
\section{What the Flux}

\begin{enumerate}[label=(\alph*)]

\item What is the net electric flux through the cylinder below?
\begin{center}
\includegraphics[width=.3\linewidth]{W2b_fig2}
\end{center}
\item What is the surface area of a sphere? What is the volume of a sphere?

\item For a symmetric sphere, prove:
$$\Phi_{e} = \oint_{S} \vec{E} \cdot \mathrm{d}\vec{A} = E\cdot4\pi r^2$$ 
	
\end{enumerate}

\section{Cylindrical Symmetry}
\begin{center}
\includegraphics[width=.3\linewidth]{W2b_fig1}
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\begin{enumerate}[label=(\alph*)]
	\item What is the surface area of the rod of length $L$?
	\item The net electric flux coming out through the cylinder is $-1000$ Nm$^2$/C. How much charge is enclosed   within the cylinder?
\end{enumerate}


\end{document}