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Question 1. Write the full set of Maxwell's equations in differential form with a brief explanation for the case of: a a (i) a static electric field, assuming that the dielectric is linear, but inhomogeneous; (ii) a static electric field produced by the charges on a set of conducting bodies situated in a vacuum; (iii) a steady current flow in a homogeneous conductor of conductivity o, with no impressed electric field; (iv) a steady current flow in an inhomogeneous poor dielectric, with impressed electric field E; present. (v) a time-constant magnetic field in a linear medium of permeability , produced by a steady current flow; (vi) a time-constant magnetic field, produced by a permanent magnet of magnetization M (a function of position); (vii) a time-constant magnetic field produced by both steady currents and magnetized matter, if the medium is not linear. (viii) a quasi-static electromagnetic field, produced by quasi-static currents in nonferromagnetic conduc- tors. (ix) an arbitrary electromagnetic field in a vacuum, no free charges being present; (x) an arbitrary electromagnetic field in a homogeneous perfect dielectric of permittivity E and perme- ability . a