hw2_p5405_f06 - defined by cos θ ≥ cos α a)What is E(0...

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HW 1 Phys5405 f06 due Sept. 7 1) JDJ chapter 1 problem 3 2) JDJ chapter 1 problem 5 3) JDJ chapter 1 problem 7 4) Consider two concentric spherical surfaces. The inner sphere has radius R and the outer radius R + δ , where δ << R . The inner surface has uniform surface charge density σ while the outer one has uniform surface charge density - σ . Accurately sketch E versus r, the distance from the center. Show that there is a discontinuous change in E as you move through each surface in the radial direction. Do the same for Φ. Let δ 0 and show Φ changes discontinuously as you go through a dipole layer. 5) Charge is uniformly spread on a spherical surface of radius = 1 m except for a region
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Unformatted text preview: defined by cos θ ≥ cos α . a)What is E (0)? When α → 0 and z → ± 1, what are E ( ± e z )? Note, in this case if you used Gauss’s law and incorrectly allowed the charge on the surface to be included in the total charge you would get a diferent (incorrect) answer. What is that answer? Now use a program like Mathematica and accurately graph E ( z e z ) vrs z for the following cases: a)z=(0,2), for cos α = 0 . 999 , ,-. 999 b)z=(0,-2) for cos α = 0 . 999 , ,-. 999 Why does E change discontinuously at z=-1 in case b, but not at z=1 in case a? 1...
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