The rotation of the conducting core of the earth in its own magnetic field generates both a v × B field and a competing electrostatic field - ∇V. These two fields together excite toroidal currents, and therefore azimuthal magnetic fields, on the condition that v and B satisfy a certain general condition within the core. Ferraro's law of isorotation is valid, but it concerns a special case. We calculate these azimuthal magnetic fields, first with the core rotating as a solid, and then differentially, with the angular velocity a function of the axial coordinate and a function of the radial coordinate. Our straightforward calculation shows that these azimuthal fields are much weaker than is usually believed. The computer codes are available from the author.