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Physics 102Fall 2014NAME:Quiz 12 - SolutionsMake sure your name is on your quiz, and pleaseboxyour final answer. Because wewill be giving partial credit, be sure to attempt all the problems, even if you don’t finishthem!1. SupposeV= 0 and~A=A0sin(kx-ωt)ˆj, whereA0,ω, andkare constants.(a) Show that these potentials satisfy theCoulomb gauge, where∇ ·~A= 0.(b) Find~Eand~Bfrom these potentials.(c) Check that your results from part (b) satisfy Maxwell’s equations in vacuum,whereρ=~J≡0. What condition must you impose onωandk?————————————————————————————————————Solution1