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Polarity Free Magnetic Repulsion and Magnetic Bound State

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Polarity Free Magnetic Repulsion and Magnetic Bound State Polarity Free Magnetic Repulsion and Magnetic Bound State Hamdi Ucar Independent Researcher, Istanbul Turkey, [email protected] This is a report on a dynamic autonomous magnetic interaction which does not depend on polarities resulting in short ranged repulsion involving one or more inertial bodies and a new class of bound state based on this interaction. Both effects are new to the literature, found so far. Experimental results are generalized and reported qualitatively. Working principles of these effects are provided within classical mechanics and found consistent with observations and simulations. The effects are based on the interaction of a rigid and finite inertial body (an object having mass and moment of inertia) endowed with a magnetic moment with a cyclic inhomogeneous magnetic field which does not require to have a local minimum. Such a body having some degrees of freedom involved in driven harmonic motion by this interaction can experience a net force in the direction of the weak field regardless of its position and orientation or can find stable equilibrium with the field itself autonomously. The former is called polarity free magnetic repulsion and the latter magnetic bound state. Experiments show that a bound state can be obtained between two free bodies having magnetic dipole moment. Various schemes of trapping bodies having magnetic moments by rotating fields are realized as well as rotating bodies trapped by a static dipole field in presence of gravity. Also, a special case of bound state called bipolar bound state between free dipole bodies is investigated. KEYWORDS: magnetic bound state, magnetic levitation, polarity free repulsion, magnetic trapping 1 Introduction Things can be bound classically by force fields they possess and inertial forces balancing them. Despite some force fields have attractive and repulsive actions, it is not possible to obtain stable equilibrium through force fields alone as proven by Earnshaw’s theorem. Therefore classically, everything to be bound should have some dynamics in order to incorporate inertial forces. The common mechanism is the orbital motion and can explain bound states of celestial bodies. Orbital bound state is also possible within electrically charged bodies and used in Bohr model of the atom based on inverse square law, but stability cannot be obtained within magnetic forces where their dependence to the distance is out of range of the power figure to obtain stable orbital motion within the central force problem [1]. This precludes orbital bound state of nucleons based on magnetic forces. While classical physics fails historically to propose a binding mechanism of nucleons, nuclear forces and additional mechanisms are introduced as part of quantum physics addressing this problem. The orbital motion based on dipole-dipole interaction was later investigated by several authors including Kozorez [2], Shironosov [3]. Here is introduced a new mechanism to obtain bound state of entities having magnetic moment, using again inertial behaviors but in a different manner. It is based on magnetic forces, using attraction force to keep entities having magnetic moments together and balance this attraction with dynamically created repulsive magnetic 1 action which might be classified as a force too. This repulsive force or the interaction is called polarity free magnetic repulsion (PFR) and the resulting bound state as magnetic bound state (MBS). Although it is possible to evaluate MBS as a dynamic equilibrium based on magnetic interaction directly without introducing PFR, generalization might be difficult. MBS might be considered as versatile because it allows entities having mass, moment of inertia and magnetic dipole moment to be bound without precise requirements. These entities can be compact bodies; that is, one body is not surrounded by the other. Fig. 1.1. A scaled-down MBS realization where a tiny fragment of a NdFeB magnet weighing about 5 mg is levitated at the tip of rotator assembly consisting of an irregular magnet fragment of ~3 mm in size coupled to a micro motor having dimensions ⌀4×10 mm running at 105000 RPM (11000 rad/s). Dynamically created repulsive action based on magnetism this way has a short range; that is, it diminishes about twice as fast by distance compared to magnetic forces between dipoles. This allows to obtain stable equilibrium between PFR and magnetic or other attractive forces in various schemes and configurations. While the mathematical model of the PFR is applied to specific configurations in this work, experiments show it is present regardless of magnetic orientations of magnetic moments of entities. Stability and other characteristics of PFR and MBS are evaluated analytically and by simulations for basic cases. These cases are extended experimentally with numerous schemes and configurations, basically by bounding two permanent magnets in terrestrial environment without a physical contact, except the ambient air. It was not possible to test the bound state of two free magnets truly (in free fall) in terrestrial environment but performed in an approximated manner. On the other hand, gravity was helpful to test the strength of bound states and some configurations allowed to obtain bound state regardless of the direction of gravity. MBS of two free bodies is also evaluated through simulations and gives confidence that it can as well be experimentally realized in space and under friction free conditions. Scalability of MBS is tested experimentally by varying mass of the trapped magnets from 0.01 to 100 g in various configurations. It should be noted that for the bound state of two free bodies, selection of moment of inertia of one body have some limitations. A known method for trapping magnetic bodies with cyclic fields [4] is based on parametric excitation and this way, the body can be kept at the local minimum of a quadrupole field. This solution is equivalent to well-known rolling marble on a rotating saddle and its dynamics can be modeled by the Mathieu equation [5]. This model is also used to trap charged particles [6]. It is also possible to trap magnetic bodies at local minimum of static or quasi-static quadrupole fields while trying to keep bodies in correct orientation in order they are pushed in the direction of the weak field. This is the main mechanism for trapping neutral atoms and particles [6, 7]. Since magnetic moments of these bodies are associated with quantum spin, they can keep their orientations parallel or anti-parallel to the field they are exposed. However, their aimed orientations can be lost or get flipped if the field becomes zero or too weak at the local minimum. This issue is addressed with different schemes. In a recently proposed scheme [8] to trap neutral particles using rotating magnetic field of an electromagnetic wave, the rotating field has a similar role of the rotating electric field in the Paul trap [6]. Solutions obtained there might be also related to [9]. 2 Another scheme is known as Levitron® [10, 11, 12] and a variation called Horizontal Levitron [13]. In the original Levitron, a rotating dipole body around its dipole axis is levitated by a repulsive magnetic interaction having positive stiffness balanced by gravity and negative stiffness introduced in angular degrees of freedom is balanced by the positive dynamic stiffness caused by the rotation and precession of the body. In the horizontal axis Levitron, the body is trapped between multiple dipole magnets. In this solution, precession of the top has a similar role. A detailed analysis of this solution can be found here [14]. Superconductivity also allows to trap objects or obtain bound state directly by handling magnetic field belonging to the object known as flux pinning; however, classical physics does not cover this phenomenon. Another mechanism to induce thrust using cyclic fields is ponderomotive force. With this scheme, it is possible to induce a net force in direction of the weak field on electrically charged particles regardless of their polarities by exposing them to an alternative electric field having a gradient. This is also a parametric excitation mechanism where a characteristics of the driven harmonic motion (DHM) called phase lag is present and the net force is produced while the particles oscillates through the gradient. Phase lag is the condition where the action and reaction are in opposite phases in a periodic excitation. An example of this in mechanics is a mass spring system driven through the spring. This mechanism also constitutes the principle of bass reflex speakers. While PFR and ponderomotive force have some similarities, the acted force in ponderomotive force has alternating cycle and a body needs to oscillate along the applied force direction but PFR can be obtained by a static interaction (including fields and forces) and within the local reference frame. PFR and MBS does not depend also on local minimum since they can be obtained between dipoles. In PFR, the repulsive force is basically produced by “antiparallel” orientation of a free body with an inhomogeneous magnetic field. Here the term antiparallel denotes an orientation where the angle between two vectors is greater than π/2. While such an orientation is unstable in magnetostatics, it can be stable within DHM under phase lag condition. The way to obtain PFR is exposing an inertial body embedded with a magnetic moment to an inhomogeneous rotating field or by spinning such a body which creates a rotating field and exposing it to an inhomogeneous static field. PFR might be explained in the basic case by two steps in a simpler way. The first step is obtaining a suitable and stable angular motion of the body induced by the torque of the rotating field through DHM. As a characteristics of the harmonic motion, the phase of the motion could be in the opposite phase of the driving field, called phase lag condition. This allows to keep the magnetic orientation of the body in some antiparallel angle (>90°) with the field.
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