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We model and analyze the effect of particle shape on the signal amplification in inductive coil magnetic resonance detection using the reversible transverse magnetic susceptibility of oriented magnetic nanostructures. Utilizing the single magnetic domain Stoner-Wohlfarth model of uniform magnetization rotation, we reveal that different ellipsoidal particle shapes can have a pronounced effect on the magnetic flux enhancement in detection configurations typical of magnetic resonance settings. We compare and contrast the prolate ellipsoids, oblate ellipsoids, and exchange-biased spheres and show that the oblate ellipsoids and exchange-biased spheres have a significantly higher flux amplification effect than the prolate ellipsoids considered previously. In addition, oblate ellipsoids have a much broader polarizing magnetic fieldrange over which their transverse flux amplification is significant. We show the dependence of transverse flux amplification on magnetic resonance bias field and discuss the resulting signal-to-noise ratio of inductive magnetic resonance detection due to the magnetic nanoparticle-filled core of the magnetic resonance detection coil.