ECE309-2008-hw3

ECE309-2008-hw3 - ECE 309 Electromagnetic Fields University...

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ECE 309 — Electromagnetic Fields University of Virginia Fall 2008 Homework # 3 — The Scalar Potential Due: Wednesday, September 17 1. Find the potential, Φ , at a distance z above the center of the charge distributions shown below: (a) (b) (c) In each case, ﬁnd ~ E = - ~ Φ and compare to the answers found previously (in homework 1 or worked out in class). Suppose that the right-hand charge in (a) is changed to - q . What then is the potential at P ? What ﬁeld does this suggest? Compare this to your answer in homework 1 and explain carefully any discrepancy. 2. Find the potential a distance r from an inﬁnitely long straight wire that carries a uniform line charge λ . Find the gradient of your potential and check that it yields the correct electric ﬁeld. 3. Suppose a charge distribution ρ 1 produces a potential V 1 ( r ) , and some other charge distribu- tion ρ 2 produces potential V 2 ( r ) . (Note that charge distribution ρ 1 may have nothing at all to do with charge distribution

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ECE309-2008-hw3 - ECE 309 Electromagnetic Fields University...

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