# How big is the Lorentz force on the Sun?

The LOFAR observations have made an estimate of the magnetic field of the Milky Way. The value in our region is very small. About 1/1000 of the Earth magnetic field.

The Earth and the Sun move at a cosiderable speed around the center of the Milky Way though. Both move with a speed of around 828 000 km/hr around the center of the Milky Way.

Now currents moving in a magnetic field experience a Lorentz force:

$$F_{l}=-qv\times B$$

Where $$q$$ is the charge, $$v$$ the speed of the charge, and $$B$$ the magnetic field the charges move in. The force is always perpendicular to the velocity.

Now on the Sun, as well as inside the Earth, there is a net current giving rise to their magnetic fields. This means there is a net current in the direction of motion around our galaxy.

How big would be the force on the Sun moving through the magnetic field of the Milky Way?

• "This means there is a net current in the direction of motion around our galaxy." I don't follow this logic. Commented Jul 2, 2021 at 23:07
• Crossposted to physics.stackexchange.com/q/651722/2451 Commented Jul 16, 2021 at 20:11

Due to the fact that electrons can escape the gravitational field of the sun more easily than ions, the sun is positively charged by an amount $$q=77$$ Coulombs (see https://www.aanda.org/articles/aa/abs/2001/24/aah2649/aah2649.html ). You can calculate the Lorentz force from this. The magnetic field of the Milky Way is however even much smaller than 1/1000 of the earth's (not sure where you go this figure from). According to this reference http://www.scholarpedia.org/article/Galactic_magnetic_fields#Magnetic_Fields_in_the_Milky_Way , the galactic magnetic field near the sun is about $$6\mu G =6\times 10^{-6}G$$. With this the Lorentz force on the sun comes out as about $$110 N$$. For comparison, the gravitational force on the sun by the galaxy amounts to about $$4\times10^{20} N$$ (see How strong is the force between the Sun and the centre of the Milky Way? ).