Electricity can come in many forms on Earth but when is amps and/or voltage limited physically on Earth? In other words, what voltage arises naturally on Earth?
The maximum voltage which can possibly occur depends on the materials involved and the distance.
When the breakdown voltage of an insulator is exceeded, the electric potential difference is large enough to force the material into becoming a conductor.
This means that for example when the voltage between two points on the surface of the earth, or two in the sky, or anywhere else connected by air, exceeds about 3kV/ḿm (depending on e.g. humidity) the air between them starts to conduct and the potential will tend to equalize. The same principle applies when the points are separated by materials such as rock.
It turns out, however, that we are not here interested in the properties of the atmosphere since lightning is insignificant compared to the geodynamo. I am not aware of any easily digestible summaries which put the numbers in terms of raw amperage, unfortunately. I did manage to find this lecture which (p. 30) has some estimates of total current in the inner magnetosphere (so in space surrounding the planet, not on it unfortunately) in the multi mega-ampere range.