If a steady (constant) current, I, is flowing through a wire lying on the z-axis , experiments show that this current produces a Amperian magnetic field in the xy-plane given by: Wire /loop Holl -y x B(x, y) = 27 Lx2 + 12 + x 2 + where Ho is a constant called the "permeability of free space". (a) Show that the divergence of the vector field is : 0 = 4 . 4 [Physically, this result says that there are no "magnetic monopoles".] (b) Let Cbe a circle ("Amperian loop") of radius R, centered at the origin in the xy- plane. Parametrizationd show that: B . dr = Hol [In physics this result is known as Ampere's Law.]