PPhysics 4321 Homework Set 11 November 17, 2008 Due: November 24, 2008 1. A circular loop of wire with radius Rlies in the x-yplane, centered at the origin. If it carries a current I, counterclockwise as viewed from the point z= +Rz^, (a) what is its magnetic dipole moment m? (b) Using the values of mfrom part (a), calculate the approximate Bfield at points far from the loop. (c) For points on the z-axis, show that your results are consistent with those from the exact field in example 5.6 when z>>R. 2. Consider the motion of a particle with mass mand electric charge qein the field of a hypothetical magnetic monopole qmat the origin where B= (µoqm/4πr2) r^. (a) Find the acceleration of the particle, expressing your answer in terms of qe, qm, m, r, and v, where rand vare the particle’s position and velocity, respectively. (b) Show that the speed v= vis a constant of the motion. 3. An infinitely long circular cylinder carries a uniform magnetization Mparallel to its axis, which is assumed to be parallel to z^. Find the magnetic field inside and outside the cylinder.
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Magnetic Field, long circular cylinder, infinitely long cylinder, bound current densities