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CourseNotes.10

# CourseNotes.10 - charge enclosed by the surface is simply...

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charge enclosed by the surface is simply the total charge on the sphere q . Hence, by Gauss’s law, the field outside must be: E = q 0 4 πr 2 which is exactly the same field as a point charge centered at the center of the sphere. Inside of the sphere the same symmetry arguments hold, but the total charge enclosed by the sphere will be proportional to the volume of the sphere. q enc = ρ V = q 4 3 πR 3 4 3 πr 3 = q r 3 R 3 Plugging this into Gauss’s law gives the electric field inside of a uniformly charged sphere. E = q 0 4 πR 3 r 4.5 Problems Problem 23.8 Figure 6 shows two nonconducting spherical shells fixed in place. Shell 1 has uniform surface charge density +6 . 0 μC m 2 on its outer surface and radius 3 . 0 cm ; shell 2 has uniform surface charge density +4 . 0 μC m 2 on its outer surface and radius 2 . 0 cm ; the shell centers are separated by L = 10 cm . In unit-vector notation, what is the net electric field at x = 2 . 0 cm ? Figure 6: Two charged shells.
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