Constants and calculated parameters

Units

Used formulas, their numbers

Calculation results

μ₀

H/m

1.26 × 10⁻⁶

Distance between the middle point of the lower mantle layer and the bottom surface, R_нм

m

6.37 × 10⁶

Radius of the lower mantle outer surface, R_D

m

5.68 × 10⁶

Lower mantle layer thickness, ΔR_D

m

1.9 × 10⁶

Spherical surface S_D area with radius R_D

m²

$S_D=4\text{π}{R}_D^2$

4.05 × 10¹⁴

Thermofield Е_T density in the lower mantle D at ΔT = 4000˚C

V/m

${Е}_T=\beta \cdot \Delta T/\Delta R_D$ , (3)

where β = 0.0003 V/deg.

1.58 × 10⁻⁷

Plank’s constant, ħ

J・s

1.05 × 10⁻³⁴

Electron concentration in a unit volume of the lower mantle ores, n

m⁻³

1.0 × 10²⁰

Electron charge, е

C

1.6 × 10⁻¹⁹

Electron mass, m_е

kg

9.1 × 10⁻³¹

Lower mantle electroconductivity, σ

S/m

0.4

Fermi momentum, p_F

m・kg/s

$p_F=\hslash {\left(3{\text{π}}^{2}n\right)}^{1/2}$ (10)

1,51 × 10⁻²⁷

Electron mean free path, l

nm

$l=\frac{\sigma \hslash {\left(3{\text{π}}^2\right)}^{1/3}}{e^2{n}^{2/3}}{10}^9$ (7)

0.237

Current density, j

A/m²

$j=e^{2}n{E}_T\frac{l}{p_F}$ (9)

6.34 × 10⁻⁸

Total amount of current of lower mantle D coming through the S_D surface, I_top

А

$I_{top}=j{S}_D$ (11)

2.57 × 10⁷

Magnetic induction on the Earth’s bottom surface $B_{ТТ}^{top}$ (according to the measurements, В₀ is 3.4 × 10⁻⁵ T on the equator)

T

$B_{ТТ}^{top}=\frac{3{\mu }_0{I}_{top}\text{Δ}{R}_D}{4\text{π}{R}_{нм}^2}\text{sin}\alpha$ (14)

4.62 × 10⁻⁶

The heat, emitted in the lower mantle by the thermocurrents I_top in a year, $Q_{lm}$

J・year

$Q_{lm}=\frac{1}{\sigma }{J}^2{V}_{lm}\Delta t$ (15)

2.84 × 10¹⁴