Constants and calculated parameters

Measure

Used formulas

Results of calculations

Т of the metal core layer: outer shell/core center

K

20000/23000

Metal core radius, $R_C$

m

1.0 ´ 10⁷

Radius of the core with the rock shell, $R_{C+S}$

m

1.3 ´ 10⁷

Thermofield intensity $E_C^T$ in the core when ΔT_С = 3000 К

V/m

$E_C^T={\beta }_{*}\Delta T_{С}/R_C$ (2)

where β = 0.0001 V/deg

3.0 ´ 10⁻⁸

Area of the core spherical surface with radius $R_C$

m²

$S_C=4\text{π}{R}_C^2$

1.26 ´ 10¹⁵

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

Core electrical conductivity, σ

S/m

110000

Concentration of electrons in the core when pressure is 4.5 ´ 10¹² GPa, 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)

1.48 ´ 10³⁰

Fermi momentum , p_F

m・kg/s

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

3.72 ´ 10⁻²⁴

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)

0.0108

Current density, $j_C$

A/m²

$j_C=e^{2}n{E}_C^T\frac{l}{p_F}$ (3)

3.3 ´ 10⁻³

Total current value through its outer surface $S_C$ , $I_C$

А

$I_C=j_C{S}_C$ (9)

4.15 ´ 10¹²

Magnetic induction on the Jupiter’s pole $B_C^p$ / Measured magnetic induction on the pole $B_{ju}^p$

T

$B_C^p=\frac{3{\mu }_0{I}_C{R}_{\text{C}}}{4\text{π}{R}_p^2}\text{sin}\alpha$ (11)

2.79 ´ 10⁻³/1.4 ´ 10⁻³

Magnetic induction on the Jupiter’s equator $B_C^e$ / Measured magnetic induction on the equator $B_{ju}^e$

T

$B_C^e=\frac{3{\mu }_0{I}_C{R}_{\text{C}}}{4\text{π}{R}_e^2}\text{sin}\alpha$ (11)

2.43 ´ 10⁻³/4 ´ 10⁻⁴