Low field MRI machines are important, since the machines offer easy access for users. However, the SNR attained with a low field MRI machine is not necessarily high. This paper attempts to present an effective resonator coil designed in particular for a human hand placed in a wrist-sized permanent magnet MRI machine. The optimal design of a solenoidal coil is investigated. The wire conductor features and the proximity to the other conductors are also investigated. A rectangular solenoidal coil was built. MR Images of the hand were obtained. The wrist contour, finger muscles, fatty tissues and bone marrow were distinctly displayed.