quiz3_2009 - ECE 107 Quiz 3 Monday March 2 2009 Name Please...

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ECE 107 Quiz 3 Monday, March 2, 2009 Name : ___________________________________ Please show all your work for more rational grading. Give you solutions as formulas. Then, substitute the given numbers for final answers. Box your answers in the form of formulas and numbers. GRADING: 1) 25 points ________________ 2) 25 points ________________ 3) 25 points ________________ 4) 25 points ________________ Total (100 points) _________________
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1) Consider a structure comprised of two coaxial perfectly conducting cylindrical shells of radii 1mm a = and 2mm b = (Fig. 1). The cylinders are infinitely long in the z dimension and have negligible thickness. The smaller cylinder is grounded (kept at zero potential) and the larger cylinder is at the potential 0 10V V = . The space between the cylinders is filled with vacuum. The potential leads to a uniform surface charge density 1 s ρ and 2 s ρ on the smaller and larger cylinder, respectively. The electric field outside the larger cylinder (i.e., for r b > ) is zero. Find the electric field distribution (note the symmetry of the problem). Find the potential distribution between the cylinders. Find the charge densities on the
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