Consider a circular conducting wire of radius r carrying a constant current i. the loop lies in the zy-plane and the center of the loop is at origin of the coordinates. the z-axis goes through the center of the loop and it is perpendicular to the plane where the loop lies. the current in the loop flows counterclockwise when viewed from a point on the 2-axis, with 2 > 0 a) from the law of biot-savart, show that the magnetic field on the z axis is (10 points) b _ir 2 (2+) tk two current loops, identical to the one described in the first part of the problem, are placed parallel to the zy-plane, one with center at (0.0, l/2) and the other with center at (0,0,-l/2), respectively. the current in each of the two loops flows counterclockwise. b) calculate the total magnetic field along the z axis. (10 points) c) shows that the derivative of the magnetic field with respect to 2 vanishes at 2 = 0. (10 points) d) calculate the second derivative of the magnetic field with respect to 10 points) e) what is the value of the ratio l/r, for which the second derivative of the magnetic field at 2 = 0 vanishes? (10 points) the fourrers