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\centerline{\bf Boundary Conditions on Electric Fields at Surfaces}
\medskip

We would like to examine how the components of an electric field change as it
crosses a charged surface (with surface charge density $\sigma$).  Use one of
the integral forms of Maxwell's equations, either
$$
\oint \EE\cdot {d\rr}=0
$$
around a ``small" rectangular loop or 
$$
\int \EE \cdot d\AA = {1\over\epsilon_0} \> Q_{\rm enc}
$$
over a ``small" box to find the discontinuity in the component of the field
assigned to your group.  You will have to decide which law to use and how to
orient your loop or box depending on the physics of the problem.

If you get done with the first example, go on to the second.

\bigskip

{\bf Odd numbered groups:}

Find the discontinuity in $E_{\perp}$, the component of the electric
field perpendicular to the surface.

\bigskip
{\bf Even numbered groups:}

Find the discontinuity in $E_{\parallel}$, the component of the electric
field parallel to the surface.

\vfill
\leftline{\it by Corinne Manogue and Kerry Browne}
\leftline{\copyright 2004 Corinne A. Manogue}
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