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VIWhen Magnetic field beats
Gravitational.
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Many asked me how iPad is being held by the chalkboard. Here is the demonstration and explanation.
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You see the presence of two fields. Gravitational and Electromagnetic. Well, here we deal with constant magnetic field, so the electric component is out of our interest.
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The equations for magnetic field are macroscopic Maxwell field equations (Landau, vol. 8). For gravitational field - Einstein field equations (Landau vol. 2), on Earth 🌎 we deal with their linearized form, so Newtonian but for the sake of generality let’s refer to Einstein’s.
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iPad cover has special metallic plates inside and gets attached to the board made of the material with ferromagnetic properties. The magnetic field beats gravitational here, it is stronger. This also shows that the radius of action of electromagnetic field is smaller than gravitational one. So at small distances (atoms) we often don’t even consider the presence of gravity (atoms in dipole traps are floating in space).
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In our example gravitational field is not negligible but still smaller, so magnetic 🧲 field wins, and iPad stays attached to the board vertically. Really convenient for educational and research purposes 😌
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Notations:
∇B = divB, ∇xB=rotB (Russian) = curlB (English)
B - magnetic induction
H - magnetic field amplitude
M - magnetization of the body
β - dimensionless function of temperature
R_{ik} - Ricci curvature tensor
R - scalar curvature
T_{ik} - the energy-momentum tensor or stress-energy tensor
Λ - cosmological constant
G - Newtonian gravitational constant
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