The source of Earth's magnetic field is a dynamo driven by convection current in the molten core. Using some basic physics principles (Maxwell's equations, fluid mechanics equations), properties of Earth (mass, radius, composition, temperature gradient, angular velocity), and properties of materials (conductivity and viscosity of molten iron) or other relevant facts, is it possible to estimate the strength of the field to order of magnitude (about one gauss)?
Descriptions I've seen of the geodynamo all refer to extensive numerical computation on a computer, but can we get a rough idea with simple estimation?