The effect of a superstrong magnetic field on neutron stars or white dwarfs is studied for Thomson scattering in a fully ionized collisionless. plasma. The equation of motion for an electron in the presence of both the induced electric field of the plasma and a static uniform external magnetic field is used to determine the acceleration of the electron. The collective plasma effects due to the field and density fluctuations are investigated by using the test-particle picture. The scattering of a photon by a plasma is a function of the acceleration of particles by the electric field of the incident wave and the static external magnetic field Assuming that the electrons are distributed with density the radiation field far from the scattering center is where the delta function indicates that all quantities are to be evaluated at the retarded time and δλ is the angle between the wave vector and the Poynting vector, which is given by