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Register a new userOn the Spinning Motion of the Hovering Magnetic Top
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In this paper we analyze the spinning motion of the hovering magnetic top. We have observed that its motion looks different from that of a classical top. A classical top rotates about its own axis which precesses around a vertical fixed external axis. The hovering magnetic top, on the other hand, has its axis slightly tilted and moves rigidly as a whole about the vertical axis. We call this motion synchronous, because in a stroboscopic experiment we see that a point at the rim of the top moves synchronously with the top axis. We show that the synchronous motion may be attributed to a small deviation of the magnetic moment from the symmetry axis of the top. We calculate the minimum angular velocity required for stability in terms of the moments of inertia and magnetic field and show that it is different from that of a classical top. We also give experimental results that were taken with a top whose moment of inertia can be changed. These results show very good agreement with our calculations.
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The existence of an internal frequency associated to any elementary particle conjectured by de Broglie is compared with a classical description of the electron, where this internal structure corresponds to the motion of the centre of charge around the centre of mass of the particle. This internal motion has a frequency twice de Broglies frequency, which corresponds to the frequency found by Dirac when analysing the electron structure. To get evidence of this internal electron clock a kind of experiment as the one performed by Gouanere et al. cite{Gouanere} will show a discrete set of momenta at which a resonant scattering effect, appears. The resonant momenta of the electron beam are given by $p_k=161.748/k$ MeV$/c$, $k=1,2,3,...$, where only, the corresponding to $k=2$, was within the range of Gouanere et al. experiment. The extension of the experiment to other values of $p_k$, would show the existence of this phenomenon.
For several configurations of charges in the presence of conductors, the method of images permits us to obtain some observables associated with such a configuration by replacing the conductors with some image charges. However, simple inspection shows that the potential energy associated with both systems does not coincide. Nevertheless, it can be shown that for a system of a grounded or neutral conductor and a distribution of charges outside, the external potential energy associated with the real charge distribution embedded in the field generated by the set of image charges is twice the value of the internal potential energy associated with the original system. This assertion is valid for any size and shape of the conductor, and regardless of the configuration of images required. In addition, even in the case in which the conductor is not grounded nor neutral, it is still possible to calculate the internal potential energy of the original configuration through the method of images. These results show that the method of images could also be useful for calculations of the internal potential energy of the original system.
The magnetic moment of a particle orbiting a straight current-carrying wire may precess rapidly enough in the wires magnetic field to justify an adiabatic approximation, eliminating the rapid time dependence of the magnetic moment and leaving only the particle position as a slow degree of freedom. To zeroth order in the adiabatic expansion, the orbits of the particle in the plane perpendicular to the wire are Keplerian ellipses. Higher order post-adiabatic corrections make the orbits precess, but recent analysis of this `vector Kepler problem has shown that the effective Hamiltonian incorporating a post-adiabatic scalar potential (`geometric electromagnetism) fails to predict the precession correctly, while a heuristic alternative succeeds. In this paper we resolve the apparent failure of the post-adiabatic approximation, by pointing out that the correct second-order analysis produces a third Hamiltonian, in which geometric electromagnetism is supplemented by a tensor potential. The heuristic Hamiltonian of Schmiedmayer and Scrinzi is then shown to be a canonical transformation of the correct adiabatic Hamiltonian, to second order. The transformation has the important advantage of removing a $1/r^3$ singularity which is an artifact of the adiabatic approximation.
In the first sections of this article, we discuss two variations on Maxwells equations that have been introduced in earlier work--a class of nonlinear Maxwell theories with well-defined Galilean limits (and correspondingly generalized Yang-Mills equations), and a linear modification motivated by the coupling of the electromagnetic potential with a certain nonlinear Schroedinger equation. In the final section, revisiting an old idea of Lorentz, we write Maxwells equations for a theory in which the electrostatic force of repulsion between like charges differs fundamentally in magnitude from the electrostatic force of attraction between unlike charges. We elaborate on Lorentz description by means of electric and magnetic field strengths, whose governing equations separate into two fully relativistic Maxwell systems--one describing ordinary electromagnetism, and the other describing a universally attractive or repulsive long-range force. If such a force cannot be ruled out {it a priori} by known physical principles, its magnitude should be determined or bounded experimentally. Were it to exist, interesting possibilities go beyond Lorentz early conjecture of a relation to (Newtonian) gravity.
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