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# F10HW01 - Problem 1.4 Each of three charged spheres of...

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Unformatted text preview: Problem 1.4 Each of three charged spheres of radius a has a total charge Q . One is conducting, one has a uniform charge density within its volume, and one having a spherically symmetric charge density that varies within its volume, and one having a spherically symmetric charge density that varies radially as r n ( n > 3). Use Gauss's theorem to obtain the electric elds both inside and outside each sphere. Sketch the behavior of the elds as a function of radius for the rst two spheres, and for the third with n = 2 ; +2. 1.4.a Conducting sphere Because charge only resides on the outside of a conductor, there is no electric eld inside: E = 0 . Outside the sphere: I ~ E ¡ d ~ A = Q " E ¡ 4 r 2 = Q " E = Q 4 " r 2 where r is the distance from the center from the sphere. 1.4.b Sphere with uniform charge density Inside the sphere: 1 E ¡ 4 r 2 = Q " 4 3 r 3 4 3 a 3 E = Qr 4 a 3 Outside the sphere, a sphere of charge Q looks the same regardless of its con guration within the sphere:...
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F10HW01 - Problem 1.4 Each of three charged spheres of...

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