| If we ever build a Beanstalk (tethered mass in geosynchronous
| equatorial orbit) will the stalk carry a current from "cutting" the
| Earth's field as it orbits?
|
| If conductive, perhaps -- remember B fields, like motion, are expressed
| in vectors, so the cross product can be zero even if both terms are not
| (they only need be parallel).

No, the Earth's magnetic field moves with the Earth - the magnetic pole
doesn't travel in a circle every day, yet it is offset from the Earth's
axis.

The Earth's magnetic field does not move with the Earth out to arbitrary
distances. In the ionosphere the field gets shaped by the interaction
of the solar wind with the internal generator of the Earth (among other
lesser influences). Your analysis is oversimplified to the point of
being flat out wrong. With all due respect: Please, try again.