Coil sensitivity is considered as the most valuable data in the parallel reconstruction of magnetic resonance imaging (MRI). In this study, a novel coil sensitivity map extraction method is introduced for spatially fixed phased array coils. The proposed technique uses the Biot-Savart law with coil internal shape information and low-resolution phase image data to form sensitivity maps. The performance of this method is tested in a parallel image reconstruction task, using the sensitivity-encoding (SENSE) technique. Under the quasi-static assumption and using the duality principle, we computed the sensitivity maps of a phased-array head coil and reconstructed full FOV images. The experiments show that the resulting image quality is higher in terms of sharpness, artifact level, homogeneity, etc. than existing methods that use sensitivity maps calculated only from low-resolution image data. Moreover, several simulations were conducted using an electromagnetic simulation software tool to theoretically prove the success of the proposed technique. Our simulation results indicate that the success of the method depends heavily on the size of the coil elements. A new method for calculation of sensitivity maps is briefly introduced, which increases image quality and homogeneity while reducing the artifacts.