Extensive air showers (EAS) have been known for over 30 years to emit pulses of radio emission at frequencies from a few to a few hundred MHz, an effect that offers great opportunities for the study of EAS with the next generation of "software radio interferometers" such as LOFAR and LOPES. The details of the emission mechanism, however, remain rather uncertain to date. Following past suggestions that the bulk of the emission is of geomagnetic origin, we model the radio pulses as "coherent geosynchrotron radiation" arising from the deflection of electrons and positrons in the earth's magnetic field. We analytically develop our model in a step-by-step procedure to disentangle the coherence effects arising from different scales present in the shower structure and infer which shower characteristics govern the frequency spectrum and radial dependence of the emission. The effect is unavoidable and our predictions are in good agreement with the available experimental data within their large margins of error.