Would ferromagnetic space debris have been magnetized by their orbit in the Earth's magnetosphere? Given a nail, and a magnet it is possible to magnetize the nail by patiently rubbing the nail until it is magnetized; albeit the field strength may be less than that of the source. 
With several score kilograms of space debris in orbit, all ferromagnetic material up there may each well have been subjected to several thousand revolutions around their primary; some sooner than the other. Would such ferromagnetic debris be magnetized by their orbit within the magnetosphere?
p.s. If yes, I would assume the material that magnetize quicker might attract those that are yet to be magnetized to form a larger mass, and so on ad infinitum. What prevents such an occurence? Is it precluded merely because of the volume of open space and the possible repulsion if the similar poles face each other? 
 A: It is likely that the orbital debri has acquired some charge (positive or negative). However, it will not attract charged particles to form a larger mass ad infinitum because of something called a Debye length.
In a plasma (collection of charged particles), there are both positive and negative charges. The magnetosphere contains such plasma. One may ask, why haven't the positive charges attracted the negative ones and why do the exist separately to this date? Because of the Debye length.
Say we place a charge +Q inside a plasma with both positive charges and negative charges. The negative charges (generally electrons) will rush to the positive charge and shield the presence of this charge from the surrounding plasma. They don't rush in ad infinitum because they are attracted to positive charges in the surrounding medium as well! So, in this manner, the entire system reaches a state of equilibrium, and the surrounding plasma is completely unaware of the existence of the +Q charge because of this Debye shielding.
In the space debris context, the space debris probably has accumulated a surface charge, but it is likely that there exists a Debye shield around this object in the form of negatively charged particles. 
Note: This phenomena is not exclusive to space debris and is an active problem to detect low-energy (< 1eV) ions. Working spacecraft too build up a spacecraft charging potential, and the creation of a Debye shield prevents these ions from reaching the detectors at the spacecraft.
