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hw2_p5405_f04 - 3a In a spherical(radius a region of space...

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HW 2 Phys5405 f04 due Sept. 9 1a) Charge is arranged on the surface of a sphere of radius R centered at the origin as follows: σ = σ 0 , if θ > α and σ = 0, otherwise. Here θ is the usual polar angle, 0 θ π . Find E (r = R, θ = 0). 1b) Let α 0. This effectively puts uniform charge density on the spherical surface. Again find E (r = R, θ = 0). Now assume (incorrectly) that in applying Gauss’s Law you can use the charge on the Gauss surface. Find E (r = R, θ = 0) from Gauss’s law. You should note that the latter result disagrees with the exact integration. This illustrates why the charge on the Gauss surface must be excluded from Gauss’s Law. 2) JDJ chapter 1 problem 5
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Unformatted text preview: 3a) In a spherical (radius a) region of space, there is a volume charge density that depends only on r the radial distance from the center of the spherical region, ρ ( r ) = rα , α is a constant. A concentric spherical conducting shell of inner(outer) radii b(c) with b > a carries net charge Q. Calculate E ( r ), Φ( a )-Φ( c ), and the charge per unit area on the outer surface of the conductor. 3b) If the shell surrounded the spherical region but was not concentric with it, what answers to part a) would be unchanged (use the center of the shell as the origin)? 4) JDJ chapter 1 problem 10 1...
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