% Griffiths (3rd ed) problem 2.36 page 101

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\textbf{\large SPHERICAL CAVITIES}
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Two spherical cavities, of radii $a$ and $b$, are hollowed out from the
interior of a (neutral) conducting sphere of radius $R$, as in the figure
below.  At the center of each cavity a point charge is placed --- call these
charges $q_a$ and $q_b$.
\begin{enumerate}[(a)]
\item
Find the surface charges $\sigma_a$, $\sigma_b$, and $\sigma_R$.
\item
What is the field outside the conductor?
\item
What is the field within each cavity?
\item
What is the force on $q_a$ and $q_b$?
\item
Which of these answers would change if a third charge, $q_c$, were brought
near the conductor?
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Griffiths 2.36

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