Recently planet Mercury鈥攁n unexplored territory in our solar system鈥攈as been of much interest to the scientific community due to recent flybys of the
spacecraft MESSENGER that discovered its intrinsic stationary
and large-scale dipole like magnetic field structure with an intensity of confirming Mariner 10 observations. In the present study, with the observed constraint of Mercury's atmospheric magnetic field structure, internal magnetic field structure is modeled as a solution of magnetic diffusion equation. In this study, Mercury's internal structure mainly consists of a stable stratified fluid core
and the convective mantle. For simplicity, magnetic diffusivity in both parts of the structure is considered to be uniform
and constant with a value represented by a suitable averages. It is further assumed that vigorous convection in the mantle disposes of the electric currents leading to a very high diffusivity in that region. Thus, in order to satisfy observed atmospheric magnetic field structure, Mercury's most likely magnetic field structure consists of a solution of MHD diffusion equation in the core
and a combined multipolar (dipole
and quadrupole like magnetic field structures embedded in the uniform field) solution of a current free like magnetic field structure in the mantle
and in the atmosphere. With imposition of appropriate boundary conditions at the core-mantle boundary for the first two diffusion eigen modes, in order to satisfy the observed field structure, present study puts the constraint on Mercury's core radius to be .
From the estimated magnetic diffusivity and the core radius, it is also possible to estimate the two diffusion eigen modes with their diffusion time scales of and 3.7 billion years respectively suggesting that the planet inherits its present-day magnetic field structure from the solar Nebula. It is proposed that permanency of such a large-scale magnetic field structure of the planet is attained during Mercury's early evolutionary history of heavy bombardments by the asteroids and comets supporting the giant impact hypothesis for the formation of Mercury.