We study a novel millimetre-scale magnetic trap for ultracold atoms, in which the current carrying conductors can be situated outside the vacuum region, a few mm away from the atoms. This design generates a magnetic field gradient in excess of \SI{1000}{G/cm} at a distance of \SI{2}{mm} from the conductors. We perform electromagnetic and thermo-mechanical characterisation using Finite Element Methods (FEM). The predicted behaviour has been verified by electrical and thermal measurements on a prototype, but has not been implemented on an apparatus with cold atoms. Operating this trap at the highest gradient allows for rapid evaporative cooling comparable to that achieved by atom chips.