Forgive my limited knowledge, but the Earth's magnetic field is created by the conductive liquid in the core and to the best I can tell organizing itself (which means separating charges?). Would this mean that the core as a whole has an electric charge?
The physical explanation for the origin of the geomagnetic field is that it is caused primarily by electric currents (moving charge) in the Earth's liquid outer core. The composition of the outer core is thought to be largely iron. The temperature in the core is above the Curie temperature of iron, which means the magnetic field of the core is not caused by ferromagnetism. A core of liquid iron would conduct electricity, therefore there can be little separation of electric charge in the outer core. The natural electric fields we observe at the surface of the Earth are primarily caused by atmospheric electricity, rather than the geomagnetism of the Earth's core.
The geomagnetic field, and eddy electrical currents in the core, cause a feedback in the system which is sometimes described as the "geodynamo." The simultaneous partial differential equations that describe the "geodynamo" are very complex, have no closed solution, and test the limits of computer simulations. Merrill et al (1998) listed ten such equations, which included Maxwell's equations, the Navier-Stokes equation, and equations describing the gravity potential, the heat flow, and many other parameters. Each equation is, in turn, dependent on the boundary conditions and the initial conductions chosen. Physicists can obtain some insight by considering solutions to special cases of the magnetic induction equation.
I recommend the book North Pole, South Pole - by Gillian Turner to geoscientists and physicists alike as an introduction to the history and significance of geomagnetism.
You don't need a separated electric charge for the Earth's core to generate a magnetic field, and you don't even need a ferromagnet. This experiment simulates the magnetic field generation by using a model of the core containing liquid sodium. Actually I'm not sure if they've got it to work yet, so maybe I should say may simulate rather than simulates.
You do need something to get the field started. In the sodium experiment it's the Earth's magnetic field passing through the experimental apparatus. However once started the motion in the liquid amplifies the field and it becomes self sustaining. In the Earth's core random thermal fluctuations in the magnetic field will be amplified to produce the field we currently have.
A while back I did try to read through the maths involved but found it out of my league, so I'm afraid I can't give you any theoretical justification for the above. Maybe someone else can comment?