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— pn Assignment 11 bck 21 1. A rectangular coil of dimensions 5.40 cm x 8.50 cm consists of 25 turns of wire and carries a current of 15.0 mA. A 0.350-T magnetic field is applied parallel to the plane of the loop. (a) Calculate the magnitude of its magnetic dipole moment. (b) What is the magnitude of the torque acting on the loop? 2. An infinitely long circular cylinder carries magnetization M parallel to its axis which is the z-axis Find J, and Ky 3. Asphere of Radius R has its center at the origin. The Magnetization is given by M=(az2+ B)k where o and B are constants. Find the magnetization current densities K., and Jy. Note: In Spherical coordinates z=r cos Unit vector k = cos 6 e,— sin 8 eg, where eg and e, are unit vectors in spherical coordinates and on the surface of the sphere n= e, 4. A sphere of radius a has its center at the origin. The magnetization is uniform and is given by M (ay? + B) j and a and are constants. Find the magnetization current densities J, and Ky, 5. Aninfinite long cylider of radius R carries forzen magnetization parallel to the axis M = Brk, B is a constant and r| the distance from the axis. There is no free current anywhere, a) Locate the bound currents. J, and K, and find the B filed b) Use ampers Law (eq 6.20, to find H and then get B from Eq. 6. 18 6. A) Ina regular household wire, current / flows (uniformly!) down a long straight conducting wire of radius R. Assume the metal is a "magnetically linear" material, with magnetic susceptibility ym . Find the magnetic field B as a function of distance s from the center of the wire (both inside and outside the wire). B) Compute the total bound current per length of the rod. (include both volume and surface bound currents.) C} What can you say about the magnetic field when you consider susceptibility? Consider both Cu wire and Al wire; what happens in each case? Would it have mattered much if we had treated this problem like a “Chapter 5 problem" and totally neglected the susceptibility of the wire? Would your answer change much if this was a current flowing inside a human body (where the conductive material is basically water)? 7. Find B and H at the center of a hollow spherical cavity carved out of a farge chunk of uniform, linear, magnetic material (susceptibility 7,,) which had (before you carved the hole) a tatal uniform field B= B, & through its volume. Before the cavity is carved, the material has a uniform Ho = (1/44,)8, - M, &. (Express your final answers in terms of By and %m Only) 
