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ECE3209-2009-hw3

# ECE3209-2009-hw3 - Plot the magnitude | ~ E | as a function...

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ECE 3209 — Electromagnetic Fields University of Virginia Fall 2009 Homework # 3 — Electric Fields and Scalar Potential Due: Friday, September 18 1. Cheng, P. 3-11 . 2. Cheng, P. 3-15 . 3. Two spheres, each of radius R and carrying uniform charge densities + ρ and - ρ , respectively, are placed so that they partially overlap. The vector from the center of the negative sphere to the center of the positive sphere is ~s . Show that the ﬁeld in the region of overlap is constant and ﬁnd its value. 4. A long coaxial cable carries a uniform volume charge density ρ on the inner cylinder (radius a ) and a uniform surface charge density on the outer cylindrical shell (radius b ). This surface charge is negative and of the right magnitude that the cable as a whole is electrically neutral. Find the electric ﬁeld in each of three regions (i) inside the cylinder ( r < a ), (ii) between the cylinders ( a < r < b ), and (iii) outside the cable ( r > b

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Unformatted text preview: ). Plot the magnitude, | ~ E | , as a function of r . 5. Find the potential, Φ , at a distance z above the center of the charge distributions shown below: (a) (b) (c) 6. Cheng, P. 3-17 . In class, we found the electric ﬁeld around an inﬁnitely long uniform line of charge by applying Gauss’s Law. This was possible because the ﬁeld in that case is a function of radial distance r only and any coaxial cylindrical surface around an inﬁnite line of uniform charge is an equipotential surface. In practice, of course, all charge sources must be of ﬁnite length and, as a result, the equipotential surfaces are not coaxial cylinders. Given a ﬁnite line of charge with uniform linear charge density λ and length L , ﬁnd the potential (with reference potential of zero at inﬁnity) on a coaxial cylindrical surface of radius R as a function of x and plot it....
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ECE3209-2009-hw3 - Plot the magnitude | ~ E | as a function...

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