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\title{{\vspace{-2cm}}110A Discussion Week 7}


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\maketitle

\section{Dielectrics and Polarization}

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

\item  Show and convince yourself (Griffiths Ex 3.9), that the electric field in the region of overlap between two \textbf{uniformly charged} spheres of radii R is

\begin{equation}
    \vec{E} = - \frac{1}{4 \pi \epsilon_0} \frac{q \vec{d}}{R^3},
\end{equation}

where q is the total charge of the positive sphere and $\vec{d}$ is the vector from the negative center to the positive center.

\vspace{1.3 in}

\item Rewrite the electric field in this region in terms of the polarization density ($\vec{P}$) of the sphere.

\vspace{1.3 in}

\item What is the potential of the two-sphere system outside of both spheres? (Exploit the symmetry of the spheres.)

\vspace{1.3 in}


\end{enumerate}


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