A hollow, spherical, conducting shell of radius R, has charge of +2.0muC distrib

Question

A hollow, spherical, conducting shell of radius R, has charge of +2.0muC distributed uniformly around its surface. This shell also contains a point charge of -2.0muC at the exact center of the sphere. Describe how you would construct two Gaussian surfaces to calculate the electric field one surface outside the spherical shell, and the other in the region between the shell and the point charge. Write the expression for the electric flux threading each of your Gaussian surfaces and for the resulting electric field in each region.

Explanation / Answer

Given radius of spherical conducting shell is R charge on spherical conducting shell is Q = 2C charge on point charge q = -2C a) construc a gaussian surface in side the conducting shell of radius r1    electric field in the region between shell and point charge is                 E = k q / r12    net charge on the shell is Q' = Q + q                                                 = 2 - 2   = 0      so electric field out side the spherical shell is zero. b) electric flux through the gaussian surface is constructed in side the shell is                    = E A                        = E ( 4r12 )                         =  (k q / r12 ) ( 4r12 )                         = q / o         electric flux through the gaussian surface is constucted out side the shell is zero.

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