Maxwell's Equation. Suppose that magnetic charges q_m are found to exist. Magnetic charges in motion would then give a magnetic current density J_m = _mv_m. Such new magnetic charges and currents should affect two of Maxwells equations.

a.) Now consider an infinite straight thin wire along the z-axis carry a steady magnetic charge current I_m. Using your new Maxwells equations, what is the resulting electric field E(r)?

b.) A square loop (side L) of normal metallic wire (i.e., no magnetic charges here) is now placed around the wire of part (a). What is the induced emf around the loop?

c.) In part (b), the resulting current carrying loop (electric current I) is a magnetic dipole producing a magnetic field B_I (z) = B_I (z) z along the z-axis, which will either reinforce or oppose the magnetic current I_m depending on the direction of I. Which direction do you think B_I(z) (and therefore I) should be, and why? Therefore, what is the correct () sign in the relevant Maxwell equation term.

d.) Will the wave equation for electromagnetic radiation in free space (i.e., with no charges and currents) be altered? Explain.