+ l Z IS solenoid Side View Top View Awire of total resistance R is made into a loop with two quarter-circles of arcs of radius a and b and two straight radial sections. The loop is contained in the xy-plane. A top view of the loop is shown in the right figure above. A very long cylindrical solenoid is placed inside the loop with its axis perpendicular to the xy-plane (its axis is parallel to the z-axis). The solenoid has n turns per unit length, radius d (where the diameter 2d is smaller than (b - a) as shown) and height h (where h =3> d) and it carries a counterclockwise current I as viewed from the +z axis. The current is increasing with time at a constant rate dI, dt point P is w. = a. Consider point P at the center of the two quarter-circles. The distance between the center of the solenoid and (Part a) What is the mutual inductance between the loop and the solenoid? Express your answer in terms of a, b, w,n, d, h, R , mu_0 for g, and alpha for @ as needed. M =| mu_0/(4*pi* d) *(pi* ar2 + 2*w*(b-a)) x (Part b) What is the magnitude, I;,4, of the induced current in the loop? Express your answer in terms of a, b, w, n, d, h, R, mu_0 for wg, and alpha for o as needed. Iing = (Part c) Calculate B, the magnetic field at point P. Express your answer in terms of @, b, w, n, d, h, R, mu_0 for g, alpha for a, hati for 1, hatj for j and hatk for k as needed. : (Part d) Calculate E, the electric field at point P. Express your answer in terms of a, b, w, n, d, h, R, mu_0 for ug, alpha for e, hati for 1, hatj for j, and hatk for k as needed. E