EPJ Plus Highlight - Electric/magnetic dipole in an electromagnetic field: force, torque and energy

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Published on 08 October 2014

How does an electric (or magnetic) dipole behave in an electromagnetic field, when its velocity becomes comparable with the speed of light?

This problem has been solved for the first time in a paper recently published in EPJ Plus, where novel relativistic effects were found. In particular, it has been shown that the concept of “hidden” momentum of magnetic dipoles in an electric field, being disputable up to date, is strongly required to derive relativistically adequate solutions. Moreover, a novel concept of “latent” momentum of electric dipole should be also involved into the description of dipoles.

As is known, the energy and momentum constitute a four-vector in the four-dimensional space-time, which obeys Lorentz transformations. Hence, the revealing of novel components of the dipole momentum leads to the appearance of related contributions to their total energy. As a result, the energy of the ultra-relativistic electric/magnetic dipole occurs essentially depending on the mutual orientation of velocity, electric (magnetic) dipole moment and electric (magnetic) field.

Finally, the role of the known relativistic effects (contraction of scale, dilation of time, Thomas-Wigner rotation of coordinate axes of the inertial reference frame in the successive space-time transformations) is disclosed, while the force and torque on a moving dipole are calculated.