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hw2_p5405_f03 - The circle lies in the xy plane with its...

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HW 2 Phys5405 f03 due 9/11/03 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). 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. 1c) What is the prediction of the Gauss law incorrectly used that was mentioned in part 2b)? 2) 2n point charges q are distributed uniformly on the circumference of a circle of radius R.
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Unformatted text preview: The circle lies in the xy plane with its center at the origin. What is, λ , the charge/length on the circle. What is E (d e z ) in terms of λ . Compare this result to the continuous uniform charge/length, λ on the circle. 3) In class the following problem was considered. A right circular cylindrical volume of radius R and length L with axis along z and one end at the origin carried a uniform volume charge density ρ . We found E ([L + D] e z ). Now suppose a similar volume with charge density-ρ was located in the region-L ≤ z ≤ 0. What is the E ([L + D] e z ) from both charge distributions? When D >> R and D >> L what is the field? 4) JDJ 1-3 5) JDJ 1-5 1...
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