Planetary Magnetic Field Strength Calculator Formula

Understand the math behind the planetary magnetic field strength calculator. Each variable explained with a worked example.

Formulas Used

Surface Magnetic Field (equator)

b_field = (1e-7) * dipole_moment / pow(planet_radius, 3)

Field (Gauss)

b_field_gauss = (1e-7) * dipole_moment / pow(planet_radius, 3) * 1e4

Polar Field

b_pole = 2 * (1e-7) * dipole_moment / pow(planet_radius, 3)

Variables

VariableDescriptionDefault
dipole_momentMagnetic Dipole Moment(A m2)7.94e+22
planet_radiusPlanet Radius(m)6371000

How It Works

Planetary Magnetic Field

A planet's magnetic field can be approximated as a dipole near the surface.

Equatorial Field

B_eq = (mu0 / 4pi) * M / R cubed

where mu0/(4pi) = 1e-7 T m/A.

Polar Field

B_pole = 2 * B_eq

Earth's dipole moment is about 7.94 x 10^22 A m2, giving an equatorial field of roughly 3 x 10^-5 T (0.3 Gauss).

Worked Example

Earth: dipole moment = 7.94e22 A m2, radius = 6.371e6 m.

dipole_moment = 7.94e+22planet_radius = 6371000
  1. 01B_eq = 1e-7 * M / R cubed
  2. 02R cubed = (6.371e6)^3 = 2.586e20
  3. 03B_eq = 1e-7 * 7.94e22 / 2.586e20
  4. 04B_eq = 3.07e-5 T = 0.307 Gauss