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3. A long straight wire of radius r = R carries a steady current I = 12. A rectangular loop is formed outside the wire, as shown, with two sides of length L parallel to the current at distances r = a and r = b from the center of the wire and the remaining sides connecting the ends radially. 1 a b 1 1 L (a) First, show that magnetic flux, º3, may be generally expressed as a line integral of the magnetic vector potential A. State clearly all steps in your reasoning. (b) Show, through an application of Ampere's Law, that the magnetic field out- side the wire is given by B μοΙ 2πι: (c) The magnetic vector potential outside the wire is given as HO! In @ 21 Find the magnetic field from the magnetic vector potential. (d) Find the magnetic flux through the rectangular loop by integration of the magnetic field B. (e) Show that the line integral of the magnetic vector potential A also provides a correct expression for the magnetic flux through the loop.