HW 01.pdf - Physics 301 Electricity and Magnetism Term 1...

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Chapter 12 / Exercise 48
Calculus
Stewart
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Physics 301: Electricity and MagnetismTerm 1, 2017/18PROBLEM SET 1: Due Friday, September 15 in classProblem 1: Divergence and Curl(a) For each of the four vector fields sketched above, which of them have nonzero divergencesomewhere? (If the divergence is nonzero only at isolated points, which point(s) would thatbe?)(b) For each of the four vector fields sketched above, which of them have nonzero curlsomewhere? (If the curl is nonzero only at isolated points, which point(s) would that be?)Problem 2: Divergence(a) Computer·r, i.e. the divergence of the vectorr.(b) What is the flux ofrthrough a spherical surface of radiusa?Problem 3: Electric fieldConsider an electric fieldE=cr/r2(Note that this is NOT the usual E-Field from a pointcharge at the origin, which readsE=c0r/r3).(a) Calculate the divergence and curl ofE. Check that the divergence satisfies the divergencetheorem.(b) What charge distribution would be needed to produce such anE-field? Describe in wordsas well as formulas. Is it physically realizable?1
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Chapter 12 / Exercise 48
Calculus
Stewart
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Problem 4: Curvilinear coordinatesA vectorvhas the same magnitude and direction at all points in space. In cartesian coor-dinates,v=lxˆx+lzˆz, wherelxandlyare constant. Expressvin spherical coordinates.Problem 5: Dipole field

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