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Recently the author reported the feasibility of envisioning a scenario where a massive permanent magnetic dipole bounces off and oscillates about an invisible horizontal magnetic net in the presence of gravity. The scenario has been revisited, modifying its physical contents. The modification embodies analysis of the impact of the induced current due to the falling magnetic dipole. The induced current counteracts the conduction current and alters the dynamics and kinematics of the motion. This rapid communication reports the recent advances.

In [

We revisit the given scenario outlined above modifying its physical content by including the induced current due to the rate of change of magnetic flux of the falling magnet through the loop. For the sake of simplicity we assume this change comes about from the variation of the axial component of the magnetic field of the magnetic dipole. This puts the characteristics of these two fields, the field of the conduction current and the field of the magnetic dipole in the same footing. The character of the azimuthal field is addressed in [

Magnetic field of the DC looping current along the symmetry axis of the loop is,

where, R, n and i_{c} are the radius of the loop, number of the turns and the conduction current, respectively.

This yields the magnitude of the magnetic force,

where µ is the magnetic moment of the permanent magnet. Equation (1) with a few modifications is written as,

This equation is to apply to a cylindrical permanent magnetic dipole of a circular base radius r and a magnetic dipole moment µ. The flux of this field through the area of the circular looping DC is. Its rate of change is the induced emf conducive the induced current, i_{ind}. Combining these pieces yields,

where R_{resistance} is the ohmic resistance of the conduction loops.

The induction current given by Equation (4) counteracts the conduction current, i_{c} modifying the force F given by Equation (2) to its effective value,

Utilizing F_{eff} the equation of motion for the permanent magnet of mass m becomes,

At first glance one realizes the order of magnitude of the second term in the brace is O(k'^{2}). Knowing the k' is small, one concludes the impact of the i_{ind} when compared to i_{c} is negligible. Therefore, the dynamics of the falling magnet is being controlled solely by the conduction current. In fact implicitly we have utilized F_{eff} = F in [

As shown in the first row of

The author analyzes the impact of the induced current on the equation of motion of a mobile permanent magnetic dipole in the presence of an inhomogeneous magnetic field of a DC. It is shown that by selecting a set of thoughtful parameters the value of the induced current effectively may interfere with the conduction current resulting in curious outcomes.