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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.

$\begin{array}{1 1} Positive \\ negative \\ \text{may be positive or negative} \\ \text{none of the above}\end{array} $

1 Answer

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 $q_1$, potential difference V is always positive.
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