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TEAL Electricity & Magnetism

SECTION : Arago's Disk     

Moving Dipole
SUBJECT: Dipole Moving Above A Conducting Plane  

The figure shows the field lines of a magnetic dipole moving to the right above a thin conducting plane. The magnetic moment vector of the dipole is perpendicular to the direction of motion also perpendicular to the normal to the conducting sheet. As the movie progresses, the dipole goes from zero speed to very high speed. Intially the region below the plane is not shielded from the magnetic field, but as time progresses and the monopole moves faster and faster, the magnetic flux below the plane is increasingly excluded from that region, with the field in advance of the dipole excluded first. At very high speeds the flux is totally excluded from the region z < 0. There is a short pause at the beginning of the movie when we hold everything fixed, and then the dipole begins to move. The camera follows the dipole so that it appears to be at rest even though it is moving faster and faster. On the plane below the monopole we show the eddy currents in the plane which are induced by the motion of the dipole.

You will need a QuickTime movie player to play the mp4 movie.

If you are interested in the details of how this is calculated, we are following the classic paper of W. M. Saslow, “Maxwell’s Theory of Eddy Currents in Thin Conducting Sheet, and Applications to Electromagnetic Shielding and MAGLEV,” Am. J. Phys. 60 (8), 693-711 (1992).