Practice Problem • Calculate the average potential over a spherical shell of radius R due to a single point charge located outside the shell.
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We need to calculate the average potential over a spherical shell of radius \( R \) due to a point charge \( q \) located outside the shell. Show more…
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A thin spherical shell of radius $R$ has total charge $Q .$ What is the electric potential at the center of the shell?
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Find the average potential over a spherical surface of radius $R$ due to a point charge $q$ located inside (same as above, in other words, only with (In this case, of course, Laplace's equation does not hold within the sphere.) Show that, in general, $$ V_{\text {ave }}=V_{\text {center }}+\frac{Q_{\text {enc }}}{4 \pi \epsilon_{0} R} $$ where $V_{\text {center }}$ is the potential at the center due to all the external charges, and $Q_{\text {enc is the total }}$ enclosed charge.
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