# How strong is Earth's magnetic field in space?

I've been searching around Google and Youtube about the strength of Earth's magnetic field. By the help of wikipedia, I have found out that it's magnitude is 25 to 65 microtesla or 0.25 to 0.65 Gauss while at the Earth's surface. In Youtube I've seen a man named Richard Garriot showed that small magnets with the size of 1 inch in diameter actually works in space and is able to align itself from Earths magnetic pole.

But here is the question. How strong is Earths magnetic field in space? is it stronger than 25 to 65 microtesla or even less? disregarding the strength of gravity, would it be strong enough to attract any sort of magnets back to the Earth? or repel it away if it's facing the similar magnetic pole?

I am also drawn by the fact that neodymium magnets has stronger magnetism with the strength of 1.4 tesla compared to Earth's 25 to 65 microtesla magnitude. If Earth is able to protect us from Solar Wind, Does that mean a neodymium magnet with the strength of 1.4 tesla and hypothetically the same size of the Earth can protect itself far much better from Solar Wind?

This questions might have sound very silly, but an answer would be wonderful and much appreciated.

How strong is Earths magnetic field in space?

At what distance? The Earth's magnetic field is roughly modeled as a tilted dipole (i.e., the magnetization axis is tilted with respect to the spin axis of rotation). The magnitude at the magnetic equator is given by the approximation: $$\lvert \mathbf{B} \rvert \left( r \right) \approx B_{o} \left( \frac{R_{E}}{r} \right)^{3} \tag{1}$$ where $R_{E}$ is the Earth's radius, $B_{o}$ is roughly 31,200 nT (i.e., the average field magnitude at the Earth's surface near the magnetic equator), and $r$ is the distance from the center of Earth.

As you can see, by the time you reach ~4 $R_{E}$ the magnetic field has dropped to ~490 nT.

would it be strong enough to attract any sort of magnets back to the Earth?

I doubt one could actually create a scenario to test this as all things in space are orbiting at several km/s. Some spacecraft do use the Earth's magnetic field for orientation/attitude control, but generally these just cause small rotations not radial forces or effective drag forces.

or repel it away if it's facing the similar magnetic pole?

I highly doubt this.

Does that mean a neodymium magnet with the strength of 1.4 tesla and hypothetically the same size of the Earth can protect itself far much better from Solar Wind?

If we had a stronger field and the source region was as large as the Earth, then yes. If you used something the size of a small refrigerator magnet then no. You could see this by changing (in Equation 1 above) $R_{E} \rightarrow r_{o} \sim 1 cm$ and $B_{o} \rightarrow b_{o} \sim 1 T$. The size of the source shrunk by ~8 orders of magnitude while the strength of the field only increased by ~5-6.

The Earth protects us from the solar wind because those particles are charged, thus they respond to a magnetic field. The Earth's magnetosphere also creates a bow shock upstream of the Earth, which provides additional protection since it slows down any inflowing particles and deflects them (due to gradients in the magnetic field).

I wrote some more details on the effects of the solar wind at https://physics.stackexchange.com/a/214509/59023.

If you put your itty bitty magnet with the 1.4 tesla field at the North Magnetic Pole, and another identical one at the South Magnetic Pole, then you would have added 1.4 tesla at each pole. There would be zero effect on the Earth's magnetic field. Like all fields you're likely to encounter, magnetic field strength depends on the distance from the source. The measurement of strength at some undefined distance from the source is not useful information. Industrial magnets use a customary distance to characterize (which I've forgotten). The magnetic field strength ON Earth's surface, has a distance to the poles dependent on latitude. Unfortunately, magnetic fields are more complicated than gravitational fields (gravity is very symmetric), and except very near the Earth, a two-pole magnet is not a good approximation of the actual shape of Earth's field.

• I suspect, it is not a very bad approximation, particularly far from the Earth. – peterh - Reinstate Monica Jul 12 '16 at 1:57
• The Earth's field can be approximated as a tilted dipole up to ~5-6 $R_{E}$ quite well. There are perturbations, of course, but to first order it is just a dipole. – honeste_vivere Jul 13 '16 at 22:05