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Time-dependent fields of a current-carrying wire
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The electric and magnetic fields of an infinite straight wire carrying a steady current which is turned on abruptly are determined using Jefimenko's equations, starting from the standard assumption that the wire is electrically neutral in its rest frame. Some nontrivial aspects of the solution are discussed in detail.
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Novel distributional Laplacians and a Coulomb-gauge problem
New distributional Laplacian identities for arsinh[a(z-b)/s] and ln[a(z-b)+sqrt(s^2+a^2(z-b)^2)] are derived and applied to solve the Coulomb-gauge Poisson equation for a uniformly moving charge.
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