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emhw09 - that B = −∇ φ “almost everywhere” By...

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Electromagnetic Theory I Problem Set 9 Due: Halloween 2011 33. Consider the magnetic feld produced by a current I in an infnitely long wire lying on the z axis −∞ < z < . a) Use symmetry arguments and Amp` ere’s law to obtain the B feld everywhere outside the wire. Express the Cartesian components oF B as explicit Functions oF x, y, z . b) By direct integration oF each component oF ∇× A = B , fnd the vector potential A For this B in Coulomb gauge, ∇ · A = 0. c) Since ∇× B = 0 “almost everywhere” we should be able to fnd a scalar potential such
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Unformatted text preview: that B = −∇ φ “almost everywhere”. By explicitly integrating the components oF this equation, fnd a candidate For φ as an explicit Function oF x, y, z . d) In view oF the Fundamental theorem oF calculus φ ( y ) − φ ( x ) = i y x d l · ∇ φ = − i y x d l · B , (1) explain how your result For part c) does not run aFoul oF Amp` ere’s law. 34. J, Problem 5.3 35. J, Problems 5.4 and 5.5 36. J, Problem 5.13 1...
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