Question

If you approximate the Earth's magnetic field as the field of a magnetic dipole, the field will decrease roughly as 1/r3, just as for an electric dipole field. If the magnetic field is 0.50×10⁻⁴ T at the Earth's surface.

Estimate the strength of the magnetic field at an altitude of 2.0 Earth radii.

Answer 1

The estimated strength of the magnetic field at an altitude of 2.0 Earth radii is approximately 1.25×10^-5 T.

When approximating the Earth's magnetic field as that of a magnetic dipole, it is assumed that the field strength decreases with distance (r) from the dipole according to an inverse cube law, similar to the electric dipole field. If the magnetic field is 0.50×10⁻⁴ T at the Earth's surface, the estimated strength of the magnetic field at an altitude of 2.0 Earth radii (2R Earth​) can be determined by applying the inverse cube law.

Using the relationship B∝ 1/r^3, where B is the magnetic field strength and r is the distance from the dipole, we find that the magnetic field at 2.0 Earth radii is approximately 1.25×10^−5T. This estimation provides insight into the expected decrease in magnetic field strength with increasing altitude from the Earth's surface.