Abstract The electromagnetic fields induced by a surface coil in a spherical phantom, having a wide range of electrical properties, is studied using numerical methods of calculation. The specific absorption rate (SAR), radiofrequency magnetic field (B 1), magnetic field energy within the phantom (E B), and the volume-averaged SAR () are calculated at 10, 63, and 200 MHz. They are analyzed with respect to dielectric constant, wavelength, and skin depth effects, which become increasingly important in high field magnetic resonance imaging (MRI) where safety and field homogeneity issues need further study. Particular attention is given to solutions representing neural tissue at each frequency. In general, the data at high field strengths have local maxima, with a quasi-harmonic behavior, when the following two resonant conditions are satisfied: 1) skin depth becomes comparable to, or larger than, the sample diameter Ds; and 2) Ds is near an integral multiple of the wavelength. These are also the solutions with maximum E B values and the least homogeneous B 1. Samples undergoing resonance at 200 MHz are shown to have important off-axis B 1 maxima (affecting field homogeneity) and large values. Some non-resonating 200-MHz phantoms, including simulations consistent with neural tissue, contain larger SAR maxima than the resonating samples, posing safety concerns in high field imaging of biologic tissue.