The Moon, Earth's Dusty Attic

Yeah, when DID the Earth's strong magnetic field start?:

Minoru Ozima of University of Tokyo and colleagues put forth an intriguing alternative.

The new scenario is based on the possibility that Earth's magnetic field was not born with the planet 4.5 billion years ago, but developed sometime thereafter when the molten iron core took on a "differential rotation," meaning the outer and inner parts of the core rotate at different rates. Nobody knows exactly how or when all that developed.

... Before the magnetic field formed, nitrogen molecules in Earth's atmosphere broke down into nitrogen ions, and ions in the outer atmosphere escaped freely to the Moon, Ozima's team figures.

Back then, Earth and the Moon were much closer than they are today, so it would have been easier for the satellite's gravity to lure the ions in.

If that's the case, then scientists should be able to find out when the magnetic field turned on by checking if the amount of nitrogen is significantly higher in lunar soil of a particular age.