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A study of the specific absorption rate (SAR) in an exposed body induced by canonical antennas is presented, with the aim of determining an upper bound for the antenna transmit power that demonstrates that a product is inherently compliant with internationally accepted radio frequency (RF) exposure limits. Starting from the fundamental limits in antenna quality factor (Q) and the corresponding bandwidth, several antenna sizes are selected, and their SAR distributions are computed using the method of moments (MoM) and finite-difference time domain (FDTD) method in the frequency range 300-3000 MHz. The threshold powers are then determined, below which the peak 1-g and 10-g averaged SAR would not exceed the limits specified in international exposure standards. From the data, simple expressions are derived to estimate the threshold power over a wide range of antenna sizes, frequencies, and distances from the body. It is demonstrated that the results presented in this paper are conservative in comparison with the measured SAR data of real products as well as other published data.