Constants and calculated parameters

Measure

Used formulas

Results of calculations

Т of the Me_H layer: the upper/the lower layer borders

K

10⁴/2.0 ´ 10⁴

Radius of the outer spherical surface of the Me_H layer, $R_{{\text{Me}}_{\text{H}}}$

m

5.75 ´ 10⁷

Thickness of the layer, $\Delta R_{{\text{Me}}_{\text{H}}}$

m

4.45 ´ 10⁷

Intensity of the thermofield $E_{{\text{Me}}_{\text{H}}}^{Т}$ in the Me_H layer when ΔT = 10000 К

V/m

$E_{{\text{Me}}_{\text{H}}}^{Т}={\beta }_{\ast }\Delta T/\Delta R_{{\text{Me}}_{\text{H}}}$ , (2)

where β = 0.0001 V/deg

2.25 ´ 10⁻⁸

Area of the spherical surface $S_{{\text{Me}}_{\text{H}}}$ with radius $R_{{\text{Me}}_{\text{H}}}$

m²

$S_{{\text{Me}}_{\text{H}}}=4\text{π}{R}_{{\text{Me}}_{\text{H}}}^2$

4.15 ´ 10¹⁶

Core radius, R_C

m

1.3 ´ 10⁷

Equatorial radius of Jupiter, R_e

m

7.15 ´ 10⁷

Polar radius of Jupiter , R_p

m

6.68 ´ 10⁷

Planck’s constant, ħ

J・s

1.05 ´ 10⁻³⁴

Electron charge, е

C

1.6 ´ 10⁻¹⁹

Electron mass, m_е

kg

9.1 ´ 10⁻³¹

electrical conductivity of the Me_H layer, σ

S/m

470

Concentration of electrons in the Me_H layer (calculated by the formula for metals), medium, n

m⁻³

$n=b{\left(5\frac{m_{е}}{{\hslash }^2}{\left(3{\text{π}}^2\right)}^{-2/3}\right)}^{3/5}{p}^{3/5}$ (7)

5.64 ´ 10²⁷

Concentration of electrons in the Me_H layer (calculated by formula, considering density Н_metall $\rho =70.8\text{kg}/{\text{m}}^{\text{3}}$ )

m⁻³

$n=\rho \frac{N_A}{A}$ (8)

4.23 ´ 10²²

Fermi momentum, p_F

m・kg/s

$p_F=\hslash {\left(3{\text{π}}^{2}n\right)}^{1/3}$ (6)

1.14 ´ 10⁻²⁶

Electron mean free path, l

nm

$l=\frac{\sigma \hslash {\left(3{\text{π}}^2\right)}^{1/3}}{e^2{n}^{2/3}}{10}^9$ (5)

49.3

Current density, $j_{{\text{Me}}_{\text{H}}}$

A/m²

$j_{{\text{Me}}_{\text{H}}}=e^{2}n{E}_{{\text{Me}}_{\text{H}}}^{Т}\frac{l}{p_F}$ (3)

1.06 ´ 10⁻⁵

Total current value of the Me_H layer, through the $S_{{\text{Me}}_{\text{H}}}$ surface, $I_{{\text{Me}}_{\text{H}}}$

А

$I_{{\text{Me}}_{\text{H}}}=j_{{\text{Me}}_{\text{H}}}{S}_{{\text{Me}}_{\text{H}}}$ (9)

4.39 ´ 10¹¹

Calculated magnetic induction on the Jupiter’s pole $B_{{\text{Me}}_{\text{H}}}^p$ / Measured magnetic induction on the pole $B_{ju}^p$

T

$B_{{\text{Me}}_{\text{H}}}^p=\frac{3{\mu }_0{I}_{{\text{Me}}_{\text{H}}}\text{Δ}{R}_{{\text{Me}}_{\text{H}}}}{4\text{π}{R}_p^2}\text{sin}\alpha$ (11)

1.23 ´ 10⁻³

/1.4 ´ 10⁻³

Calculated magnetic induction on the Jupiter’s equator $B_{{\text{Me}}_{\text{H}}}^e$ / Measured magnetic induction on the equator $B_{ju}^e$

T

$B_{{\text{Me}}_{\text{H}}}^e=\frac{3{\mu }_0{I}_{{\text{Me}}_{\text{H}}}\text{Δ}{R}_{{\text{Me}}_{\text{H}}}}{4\text{π}{R}_e^2}\text{sin}\alpha$ (11)

1.15 ´ 10⁻³

/4.2 ´ 10⁻⁴