Electromagnetic Control of the Gravitational Mass of a Ferrite Lamina, and the Gravity Acceleration above it

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Ferrite Lamina, and the Gravity Acceleration above it

Fran de Aquino

To cite this version:

Fran de Aquino. Electromagnetic Control of the Gravitational Mass of a Ferrite Lamina, and the

Gravity Acceleration above it. 2019. �hal-01956680v2�

Electromagnetic Control of the Gravitational Mass of a Ferrite Lamina, and the Gravity Acceleration above it.

Fran De Aquino

Professor Emeritus of Physics, Maranhao State University, UEMA.

Titular Researcher (R) of National Institute for Space Research, INPE Copyright © 2018 by Fran De Aquino. All Rights Reserved.

Here we show that it is possible controlling the gravitational mass of a specific ferrite lamina, and the gravity acceleration above it, simply applying an extra-low frequency electromagnetic field through it.

Key words: Gravitational Interaction, Gravitational Mass, Gravity Control.

1. Introduction

In a previous paper [1] we shown that there is a correlation between the gravitational mass, , and the rest inertial mass , which is given by

m g m _{i 0}

( ) 1 1

1 2 1

1 1

2 1

1 1

2 1

2 2

2 2 0

2

0 0

⎪⎭

⎪ ⎬

⎫

⎪⎩

⎪ ⎨

⎧

⎥ ⎥

⎦

⎤

⎢ ⎢

⎣

⎡ ⎟⎟ ⎠ −

⎜⎜ ⎞

⎝ + ⎛

−

=

⎪⎭ =

⎪ ⎬

⎫

⎪⎩

⎪ ⎨

⎧

⎥ ⎥

⎦

⎤

⎢ ⎢

⎣

⎡

⎟⎟ −

⎠

⎜⎜ ⎞

⎝ + ⎛

−

=

⎪⎭ =

⎪ ⎬

⎫

⎪⎩

⎪ ⎨

⎧

⎥ ⎥

⎦

⎤

⎢ ⎢

⎣

⎡ ⎟⎟ ⎠ −

⎜⎜ ⎞

⎝ + ⎛ Δ

−

=

=

c Wn

c m

Un c m

p m

m

r i

r i i

g

ρ χ

where is the variation in the particle’s kinetic momentum; is the electromagnetic energy absorbed or emitted by the particle; is the index of refraction of the particle; W is the density of energy on the particle ;

Δ p U

n

r

( ^{J / kg} ) ρ is the matter density ( ^{kg m}

³

) ^and c is the speed of light.

The instantaneous values of the density of electromagnetic energy in an electromagnetic field can be deduced from Maxwell’s equations and has the following expression

( ) ²

2 2 2 1 2

1

E H

W = ε + μ

where E = E

_m

sin ω t and H = H sin ω t are the instantaneous values of the electric field and the magnetic field respectively.

It is known that B = μ H , E B = ω k

_r

[2] and

( ) ( ) ³

1 2 1

2

⎟ ⎠ ⎞

⎜ ⎝

⎛ + +

=

=

=

ωε μ σ

κ ε ω

r r r

c dt

v dz

where is the real part of the propagation vector

k

r

k r

(also called phase constant);

i

r

ik

k k

k = r = +

; ε , μ and σ , are the electromagnetic characteristics of the medium in

which the incident (or emitted) radiation is propagating ( ε = ε

_r

ε

₀

; ε

₀

= 8 . 854 × 10

⁻¹²

F/ m ;

μ

0

μ

μ =

_r

where ). From Eq.

(3), we see that the index of refraction m /

7

H

0

= 4 π × 10

⁻

μ

v c n

_r

= is given by

( ) 1 ( ) 4

2 1

2

⎟ ⎠ ⎞

⎜ ⎝

⎛ + +

=

= ε

_r

μ

_r

σ ωε

r

v

n c

Equation (3) shows that ω κ

_r

= v . Thus, v

k B

E = ω

_r

= , i.e., H v vB E = = μ

Then, Eq. (2) can be rewritten as follows

( ) 5 1

1

2 2 2

1

2 2 2

2 1 2 1

2 2

2 1 2 1

v E v E E

v E E

W

⎟⎟ ⎠

⎜⎜ ⎞

⎝

⎛ +

=

⎟⎟ =

⎠

⎜⎜ ⎞

⎝ + ⎛

=

⎟⎟ =

⎠

⎜⎜ ⎞

⎝ + ⎛

=

ε μ ε μ

μ μ ε

For σ >> ωε , Eq. (3) gives

( ) ⁶

2

2

2

2

σ μ ω μσ

ω ⇒ =

= v

v

Substitution of Eq. (6) into Eq. (5) gives

( )

²

2

1

2 E

W = ε + σ ω . Since σ >> ωε , i.e.,

ε ω

σ >> , then we can write that

( 2 )

²

( ) 7

2

1

E

W ≅ σ ω

Substitution of Eq. (7) into Eq. (1), yields

( ) ⁸

1 10

758 . 1 1 2 1

256 1 1 2 1

4 1 4 1 2 1

0 4

3 2

3 27

0 4

3 2

3 2

3 0

2 0 3 4 2

i r

i r

i g

m f E

m f E

c E m c f

m

⎪⎭

⎪ ⎬

⎫

⎪⎩

⎪ ⎨

⎧

⎥ ⎥

⎦

⎤

⎢ ⎢

⎣

⎡ ⎟⎟ ⎠ −

⎞

⎜⎜ ⎝

× ⎛ +

−

=

⎪⎭ =

⎪ ⎬

⎫

⎪⎩

⎪ ⎨

⎧

⎥ ⎥

⎦

⎤

⎢ ⎢

⎣

⎡ ⎟⎟ ⎠ −

⎞

⎜⎜ ⎝

⎟ ⎛

⎠

⎜ ⎞

⎝ + ⎛

−

=

⎪⎭ =

⎪ ⎬

⎫

⎪⎩

⎪ ⎨

⎧

⎥ ⎥

⎦

⎤

⎢ ⎢

⎣

⎡ ⎟⎟ ⎠ −

⎜⎜ ⎞

⎝ + ⎛

−

=

−

ρ σ μ ρ

σ μ π μ

π ρ σ μ

Note that if E = E

_m

sin ω t .Then, the

average value for E

²

is equal to

¹₂

E

_m²

because E varies sinusoidaly ( is the maximum value for

E

m

E ). On the other hand, we have E

_rms

= E

_m

2 . Consequently, we can change E

⁴

by , and the Eq. (8) can be rewritten as follows

4

E

rms

( ) 9 1

10 758 . 1 1 2

1

_{2 3} ⁴ ₀

3 27

i rms r

g

E m

m f

⎪⎭

⎪ ⎬

⎫

⎪⎩

⎪ ⎨

⎧

⎥ ⎥

⎦

⎤

⎢ ⎢

⎣

⎡ ⎟⎟ ⎠ −

⎜⎜ ⎞

⎝

× ⎛ +

−

=

⁻

ρ σ μ

Also, it was shown in the previously mentioned paper [1] that, if the weight of a particle in a side of a lamina is P r m

_g

g r

= ( g r perpendicular to the lamina) then the weight of the same particle, in the other side of the lamina is P r ′ = χ m

_g

g r , where χ = m

_g^l

m

_i^l₀

( and are respectively, the gravitational mass and the rest inertial mass of the lamina). Only when

l

m

g l

m

i₀

= 1

χ , is that the weight is equal in both sides of the lamina. Thus, the lamina can control the gravity acceleration above it, and in this way, it can work as a Gravity Controller Device.

Since the gravitational mass of a body above the lamina is , then we can conclude that

0 i

g

m

m =

( ) ^g

m

P ′ =

_i0

χ . Therefore, this means that the gravity acceleration above the lamina is

( ) 10 g

g ′ = χ

Here we show that it is possible controlling the gravitational mass of a ferrite lamina, and the gravity acceleration above it ( χ ^g ) , simply applying an extra-low frequency electromagnetic field through it, according to Eq.(9) and Eq. (10).

2. The Device

Ferrites are ceramic materials electrically non-conductive [3]. Usually all ferrites are electrically insulator (the electrons in ferrites are not free [4]). But the order of resistivity is different for different ferrites. The resistivity of ferrites varies in the range of 10

^-3

ohm-cm to 10

¹¹

ohm-cm ( 10

⁵

S m to 10

⁻⁹

S m ), at room temperature [5].

Consider a ferrite lamina with

thickness 200mm, width and 200mm length;

coated with a insulating paint, and with the

following characteristics: ;

mm 2

/

3

5000 kg m ρ =

= 5000

μ

r

; σ = 2 × 10

³

S / m . Applying across the above mentioned ferrite lamina an oscillating

electric field, E

_rms

, with extra-low frequency, Hz

f = 1 (See Fig.1), then according to Eq. (9), we get

[ ]

{ ^{1 2 1 2 . 8 10 1} }

0

^{( ) 11}

4

21

i rms

g

E m

m = − + ×

⁻

−

For a maximum electric field, E

_rms^max

, given by

( ) 12 10

8 . 1

180

⁵

max

V mm V m

E

_rms

= = × Eq. (11) gives

( ) ¹³

− 1

≅

= m

_g

m

_i

χ

Considering the value of the maximum electric field ( 180 V mm ), and that the ferrite lamina has 2mm thickness, then, in order to obtain the above result, the breakdown voltage of the ferrite lamina must be greater than 360 V , i.e., ( ≳ 360V) . This is a low breakdown voltage for a ferrite because several of them have breakdown voltage of the order of some kV and maximum electric field of some kV / mm [6].

Figure 1 shows an experimental set up in order to verify the decreasing of the Gravitational Mass of the ferrite lamina, and the decreasing of the gravity acceleration above the ferrite lamina. The ferrite lamina is attached over one of the plates of a parallel plates capacitor (See Fig.1).Under these conditions, the electric field close to the capacitor plate ( E = q 2 S ε

0

) , is the electric field across the ferrite, E

_ferrite

, i.e.,

( ) ( ) 14

2 2

2

2

_{0 0 0}

d

V S

V d S S

CV S

E

_ferrite

q

^r

ε

^r

ε ε ε

ε ^{= = =}

=

where ε

_r

is the relative permittivity of the dielectric of the capacitor; is the voltage difference between the plates of the capacitor, and the distance between them.

V d

Since E

_rms^max

= 1 . 8 × 10

⁵

V m , then in order to obtain E

^max_ferrite

_{( )}

_rms

= E

_rms^max

, we must have

( ) 1 . 8 10 ( ) 15

2

5 max

max

max

E V m

d

E

_{ferrite rms}

= ε

^r

V

^rms

=

_rms

= ×

If ε

_r

= 2 . 03 (Teflon), and , then Eq.

(15) shows that the maximum voltage difference between the plates of the capacitor must be given by

mm d = 1

rms

( ) 16 34

.

max

177

V V

_rms

=

The concepts here developed can also

be useful to build a Gravitational Motor,

which can convert the Gravitational Energy

into Rotational/Electric Energy (See Fig.2).

TEFLON ALUMINUM

+ INSULATING PAINT

FERRITE

σ =

2000

S/m

μ

_r =5000

ALUMINUM + INSULATING PAINT

TEFLON

200 mm

200 mm

2 mm

1 mm 1 mm 1 mm

1 mm

Parallel Plate Capacitor

Fig. 1 – Experimental s et up for controlling the Gravitational Mass of the Ferrite Lamina, and the Gravity acceleration above it. Note that the Ferrite Lamina has inertial mass m

_i

₍

_ferrite

₎ = 0 . 20 × 0 . 20 × 2 × 10

⁻³

× 5000 = 0 . 4 kg . Thus, the precision balance must have resolution of 0.01g or less.

Proof mass ( ) ( ) g m

P =

_{g p}

χ

< 1 χ

Dynamometer

Generator Frequency =

1Hz

(Sine)

Max. Voltage = 200Vpp

χ g χ

( ) p

m g

V

Ferrite

g Parallel Plate

Capacitor

Precision balance

Resolution: 0.01g

( ^m ) ^g

P r

_ferrite

= −

_g

r

(a)

(b)

Fig. 2 – (a) Gravitational Motor - Conversion of Gravitational Energy into Rotational Energy/Electric Energy.

(b) Gravitational Spacecraft – Gravitational Thrust. If m

_s

₍

_ferrite

₎ becomes negative, i.e., if χ < 0 , and χ > m

_i0

_{( )}

_S

m

_i0

₍

_ferrite

₎ , ( m

gS

₍

ferrite

₎ > m

gS

) then, the gravitational forces F r

₂₁

and F r

₁₂

become repulsive. Note that the gravity inside the spacecraft can be made equivalent to the gravity on the Earth

( ^{g = 9 . 8 m . s}

⁻²

) , simply putting on the spacecraft floor a set of n ferrite plates (inside the parallel plates of capacitors). In this case, the gravity above the set of ferrite plates will be ^G ( ^m

g

^r

²

)

χ

n

(See Eq. (10)). Thus, for example, if G ( m

_g

r

²

) ≈ ¹⁰

⁻¹¹

the gravity on the floor can be made of the order of 10 m . s

⁻²

by making

= 12

n and χ ≅ 10 . Ferrite with negative

gravitational mass

Ferrite with positive gravitational mass

g m P r

_ferrite

=

_g

r

g r Parallel Plate

Capacitor

Parallel Plate Capacitor

Spacecraft

( )

( ) _{( ) μ}

2 ˆ

2 12

21 r

m m

G m F

F

^gS

+

^{g ferrite g}

−

=

−

= r r

F r 21

F r 12 1

2 Ferrite

(

ferrite

)

i

(

ferrite

)

g

m

m = χ ₀

( ) 2 i 0 ( ) 2

g m

m =

( ) S i

gS m

m = ₀

( ) gS g ( ferrite )

g m m

m ₁ = +

References

[1] D

of the Relativistic Theory of Quantum Gravity, e Aquino, F. (2010) Mathematical Foundations

Pacific Journal of Science and Technology,11 (1), pp. 173-232.

Available at https://hal.archives-ouvertes.fr/hal- 01128520

[2] Halliday, D. and Resnick, R. (1968) Physics, J. Willey &

Sons, Portuguese Version, Ed. USP, p.1118.

[3] Carter, C. Barry; Norton, M. Grant (2007).

Ceramic Materials: Science and Engineering.

Springer. pp. 212–15.

[4] Verenkarv, V., (1997) PhD Thesis, chapter IV, p.203 (Electrical properties).

[5] L.G.Van Uitert (1956), Proc. I.R.E. 44, 1294.

[6] Curry, R et al., (2016) Development of Metamaterial

Composites for Compact High Power Microwave

Systems and Antennas, University of Missouri-

Columbia, Center for Physical and Power Electronics

Electrical and Computer Engineering, p. 65.