\[I=\tan^{-1}(2\tan\lambda)\]
Variables
Imagnetic inclination angle (rad)
lambdamagnetic dipole latitude (rad)
Description
What is this formula?
This formula calculates the magnetic inclination angle produced by an ideal dipole magnetic field as a function of magnetic latitude.
When to use it
Use this equation in geomagnetism and planetary science when estimating the inclination of magnetic field lines relative to the horizontal surface.
Example
Calculate the magnetic inclination at a dipole latitude of 35°.
Data:
lambda = 35° = 0.611 rad
Formula:
I = atan(2*tan(lambda))
Substitution:
I = atan(2*tan(0.611))
Result:
I = 54.5° = 0.951 rad
Applications
- Earth's magnetic field modeling
- Compass correction studies
- Space physics
- Planetary magnetosphere analysis
- Geophysical surveying