Tuesday, September 23, 2014

Levitating Stones

From the post "Wait A Magnetic Moment" and the correction made in "Erratum, 2D Flat and Flatulent",

The magnetic moment of an electron in orbit,

\(S_e=\sqrt{2}qc r_{es}\)

If  \(r_e\) has a time component,

\(r_e=r_{eo}e^{i\omega t}\)

then

\(S_e=\sqrt{2}qc.r_{eo}e^{i\omega t} \)

and  \(S_e\)  will resonate as  \(r_e\) at,

\(\omega^2_o= \cfrac { d\, r_{ e } }{ d\, T } \cfrac{\partial}{\partial\,r_e}\left(\cfrac { d^{ 2 }T }{ dt^{ 2 } }\right) \)

From the post "Gravity Wave and Schumann Resonance",  Earth has a gravity wave at 7.489 Hz and Schumann resonances at 7.83 Hz.

If, assuming no damping,

\(\cfrac { d\, r_{ e } }{ d\, T } \cfrac{\partial}{\partial\,r_e}\left(\cfrac { d^{ 2 }T }{ dt^{ 2 } }\right)=7.83^2\)

is applied to a magnetic material where the electron moment is aligned into magnetic domains, we might just have a levitating magnet or lodestone.

\(\cfrac { d^{ 2 }T }{ dt^{ 2 } }\)  is probably provided by a heat source or indirectly by a electric charge.

\(\cfrac { d\, r_{ e } }{ d\, T }\)  is characteristic of the material dependent on temperature.

At the right combination of  a heat source and temperature, the material will levitate.

If a electrical voltage is to provide for  \(\cfrac { d^{ 2 }T }{ dt^{ 2 } }\) then from the post "Rectified Waveform To The Rescue",

\(\left|\cfrac { d^{ 2 }T }{ dt^{ 2 } }\right|=\omega_dT_o\)

where  \(T_o=V_oI_ocos(\theta)\),  \(cos(\theta)\) is the power factor,  and  \(V(t)=V_oe^{i\omega_d t}\).

It is unknown how the material will behave, however we can replace,

\(\cfrac{\partial}{\partial\,r_e}\left(\cfrac { d^{ 2 }T }{ dt^{ 2 } }\right)\)

with

\(\omega_dT_o M_{t2}=\cfrac{\partial}{\partial\,r_e}\left(\cfrac { d^{ 2 }T }{ dt^{ 2 } }\right)\);

that is factor  \(\omega_dT_o\) can be distilled.  \(M_{t2}\) can be considered a material characteristic.

We have

\(\left|\cfrac { d\, r_{ e } }{ d\, T }\right|\omega_dT_oM_{t2} =7.83^2\)  or

\(\omega_d=7.83^2.\cfrac{1}{\left|\cfrac { d\, r_{ e } }{ d\, T }\right|M_{t2}V_oI_ocos(\theta)}\)

instead.

At a suitable cold temperature, adjust  \(\omega_d\) as per above expression until the magnet/lodestone  levitate.  Make sure that the material is correctly orientated, that the magnetic domains, North pole, is downward.