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4321_HW11FA08 - Physics 4321 Homework Set 11 Due 1 A...

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P Physics 4321 Homework Set 11 November 17, 2008 Due: November 24, 2008 1. A circular loop of wire with radius R lies in the x - y plane, centered at the origin. If it carries a current I , counterclockwise as viewed from the point z = + R z ^ , (a) what is its magnetic dipole moment m ? (b) Using the values of m from part (a), calculate the approximate B field 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 m and electric charge q e in the field of a hypothetical magnetic monopole q m at the origin where B = ( µ o q m /4 π r 2 ) r ^ . (a) Find the acceleration of the particle, expressing your answer in terms of q e , q m , m , r , and v , where r and v are the particle’s position and velocity, respectively. (b) Show that the speed v = v is a constant of the motion. 3. An infinitely long circular cylinder carries a uniform magnetization M parallel to its axis, which is assumed to be parallel to z ^ . Find the magnetic field inside and outside the cylinder.
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