A uniformly charged insulating sphere with radius r and charge +Q lies at the center of a thin-walled hollow cylinder with radius R > r and length L > 2r. The cylinder is non-conducting and carries no net charge. (a) Determine the outward electric flux through the rounded “side” of the cylinder, excluding the circular end caps. (b) Determine the electric flux upward through the circular cap at the top of the cylinder. (c) Determine the electric flux downward through the circular cap at the bottom of the cylinder. (d) Add the results from parts (a)–(c) to determine the outward electric flux through the closed cylinder. (e) Show that your result is consistent with Gauss’s law.
A uniformly charged insulating sphere with radius r and charge +Q lies at the center of a thin-walled hollow cylinder with radius R > r and length L > 2r. The cylinder is non-
(a) Determine the outward electric flux through the rounded “side” of the cylinder, excluding the circular end caps.
(b) Determine the electric flux upward through the circular cap at the top of the cylinder.
(c) Determine the electric flux downward through the circular cap at the bottom of the cylinder.
(d) Add the results from parts (a)–(c) to determine the outward electric flux through the closed cylinder.
(e) Show that your result is consistent with Gauss’s law.
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