The strength of the Earth's magnetic field isn't something that depends on the thing you're testing it with. The forces and accelerations due to the Earth's magnetic field change though [pedantic language point].
I really don't understand magnetism, despite knowing enough mathematics to model quite a lot of phenomena caused by it.
Where does the magnetic force come from? Or how do we predict it?
F=qvXB I know, but what are the q's and v's in a paper clip that gets stuck to a magnet?
(Free electrons?)
For the electrostatic charge, we can say "Right, this thing is + and that thing is -, so they should both experience a coulomb force towards each other". Norths attract souths is the analogue, but both also attract paper clips.
What's that about?
Where does "norths attract souths" appear in the equations anyway? What is a north pole?
(I seem to remember, once had a problem on a sheet that asked to prove that a magnetic dipole is like a tiny circuit loop...but I never did it and don't remember the answer x.x)