The Maxwell equation and the transformer equivalent-circuit model are applied to a radio frequency planar inductively coupled plasma. The spatial distribution of the vector potential, the magnetic field, and the electric field are obtained analytically. As a result, the plasma current, the mutual inductance between the coil and the plasma, and the self inductance of plasma are found to increase with increasing skin depth. The spatial distribution of absorbed power has maximum where the antenna coil exists, and has a similar profile to that of the induced electric field. The power transfer efficiency is found to increase with increasing gas pressure before a saturation around p+ 20mTorr, while it shows an increase with the plasma density before a slight decrease around a density of $5 imes10^{11}/ extrm{cm}^3$.