Charged particles are not magnetic. The electric current caused by the electric current creates a magnetic field. Basic electrical magnetic property. There is a magnetic field because there is an electric current traveling through the atmosphere which does impose an electric charge on suspended insulated objects in addition to the induced electric current in conductors on and in the ground.
The amount of induced current is directly related to the rate of flux change producing an AC current provided one end of the conductor is grounded. At the low currents and large area of very long lines, this AC component is relatively low in relation to the DC current brought in at the poles seperated by our earth's magnetic field. A static magnetic field does not induce a current. A steady DC current does build high currents in long suspended conductors.
Even high voltage transmission lines are now protected by adding a resistor to the center tap of a 3 phase transformer to ground to limit induced current. The transformers already MUST have a ground refrence already due to the DC charging of the lines that would happen if there were no ground. This is why transmission lines never use Delta transformer to Delta transformer. One or both ends of a transmission line have a substation with a Y connection with the center tap grounded.
I know of one BPA line that is Delta to Delta, but in addition to this there is a 3 phase Y transformer to nowhere that only porvides the required ground for the line.
Grounding both ends with a low impedance ground is good for lightning strike protection, but bad in a geomagnetic storm. Ungrounded is bad for line charging and lightning protection. UTP network cable is ungrounded at both ends and are subject to high voltage charging in short lengths.