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What is the formula for levitation?

Whether an object will or will not levitate in a magnetic field B is defined by the balance between the magnetic force F = M?B and gravity mg = ?V g where ? is the material density, V is the volume and g = 9.8m/s2. The magnetic moment M = (?/ µ0)VB so that F = (?/µ0)BV?B = (?/2µ0)V?B2.



In a scientific context, "levitation" isn't a single magical formula but rather a set of physical equations depending on the method used (magnetic, acoustic, or optical). For the most common form, Magnetic Levitation (Maglev), the goal is to balance the force of gravity (Fg​=mg) with a magnetic force (Fm​). The simplified nonlinear equation for a magnetic ball suspension is: mx¨=mg−x2ki2​ In this formula, m is the mass, g is gravity, k is a constant determined by the electromagnet's properties, i is the electrical current, and x is the distance between the magnet and the object. To achieve stable levitation, the upward magnetic force must exactly equal the downward gravitational pull (mg=x2ki2​). Another method is Acoustic Levitation, which uses sound waves to create a standing wave. The formula involves the Radiation Pressure (P), where the force is calculated as F=cP⋅A​, where A is the area and c is the speed of sound. In both cases, the "formula" is essentially an equilibrium of forces where an upward pressure or field perfectly negates the object's weight, usually requiring a feedback loop or a "trap" (like a Paul trap for ions) to keep the object from drifting sideways.

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Levitation is accomplished by providing an upward force that counteracts the pull of gravity (in relation to gravity on earth), plus a smaller stabilizing force that pushes the object toward a home position whenever it is a small distance away from that home position.

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Electrostatic levitation is the process of using an electric field to levitate a charged object and counteract the effects of gravity.

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