didnt know what we can and cant pick up from space. I do know we can read a license plate from the keyhole satellite despite the fact that there are many brighter light sources on the planet's surface. Also, magnetic anomaly detectors can detect very slight magnetic anomalies in the ocean (i.e. submarines) despite the fact that the earth's magnetic field is weak. Likewise, I inferred that we could measure a perturbation in the magnetsosphere which is many times weaker than the more potent but much more localized magnetic field of the LHC..
As for affecting the earths rotation, why not? After all, is it not the flow of the mantle that is theorized to generate the earth's magnetic field? Would then a magnetic field not influence the flow of the mantle? Even if we are above the curie point, the magnetic eddies (just like the ones that occur in the paramagnetic metal, aluminum, when it moves through a magnetic field) could deflect the flow of the mantle. Changing the mantle flow changes the angular momentum and this would lead to a change in the angular momentum (rotation) of the earth.
As for affecting the earths rotation, why not? After all, is it not the flow of the mantle that is theorized to generate the earth's magnetic field? Would then a magnetic field not influence the flow of the mantle? Even if we are above the curie point, the magnetic eddies (just like the ones that occur in the paramagnetic metal, aluminum, when it moves through a magnetic field) could deflect the flow of the mantle. Changing the mantle flow changes the angular momentum and this would lead to a change in the angular momentum (rotation) of the earth.