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A small sphere of radius r_{1} and charge q_{1} is enclosed by a spherical shell of radius r_{2} and charge q_{2}. Show that if q_{1} is positive, charge will necessarily flow from the sphere to the shell (when the two are connected by a wire) no matter what the charge q_{2} on the shell is.

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#### Solution

According to Gauss’s law, the electric field between a sphere and a shell is determined by the charge q_{1 }on a small sphere. Hence, the potential difference, V, between the sphere and the shell is independent of charge q_{2}._{ }For positive charge q_{1}, the potential difference V is always positive.

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