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# ps6 - Physics 880.06 Problem Set 6 Due Tuesday by 11:59 P M...

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Physics 880.06: Problem Set 6 Due Tuesday, May 24, 2011 by 11:59 P. M. Note: please turn these problems by Tuesday, May 24, at 11:59 P. M. 1. Consider a single Abrikosov vortex parallel to the z axis. Assume that this vortex experiences three forces. The first is a “Magnus” force due to an applied uniform ac current density, J ac ( t ) = J ac ˆ x cos( ωt ). The second is a frictional force F f = - η v , where v is the velocity. The last is a “pinning” force F pin = - k r per unit vortex length, where r = ( x,y ) is the two dimensional vector describing the position of the vortex in the xy plane and k is a pinning constant. (a). Find the vortex velocity v ( t ). (Consider only the vortex velocity induced by the applied current J .) (b). Suppose the current density is instead J ac x cos( ωt ) + ˆ y sin( ωt )). Find the vortex velocity in this case. (c). Describe the vortex orbit in each case. (d). Would either of the motions (a) or (b) produce a dc electric field? An ac electric field?

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