hw2_p5405_f07 - ≤ θ ≤ π Find E(r = R θ = 0 2b Let α...

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HW 2 Phys5405 f01 due 9/14/2007 Friday 1a) Given a volume charge density, Q V , that is non-zero in a cylindrical region of space with radius R and length L . Let the center of the cylindrical region be the origin. In this region Q V = Q 0 V ρ/R , where Q 0 V is a constant volume charge density. Find the potential at any point on the z axis. 1b) Very far from the region of charge density, z >> R and z >> L , what is the potential? 2a) 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
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Unformatted text preview: ≤ θ ≤ π . Find E (r = R, θ = 0). 2b) Let α → 0. This effectively puts uniform charge density on the spherical surface. Again find E (r = R, θ = 0). You should find a field different from what the Guass law would predict if the charge on the volume’s boundary surface was included in the Gauss integral. That is why such charge must be excluded. 2c) What is the prediction of the Gauss law incorrectly used that was mentioned in part 2b)? 3) JDJ chapter 1 problem 6 1...
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