We studied the magnetic interaction between circular Janus magnetic particles suspended in a Newtonian fluid under the influence of an externally applied uniform magnetic field. The particles are equally compartmentalized into paramagnetic and nonmagnetic sides. A direct numerical scheme is employed to solve the magnetic particulate flow in the Stokes flow regime. Upon applying the magnetic field, contrary to isotropic paramagnetic particles, a single Janus particle can rotate due to the magnetic torque created by the magnetic anisotropy of the particle. In a two-particle problem, the orientation of each particle is found to be an additional factor that affects the critical angle separating the nature of magnetic interaction. Using multiparticle problems, we show that the orientation of the particles has a significant influence on the dynamics of the particles, the fluid flow induced by the actuated particles, and the final conformation of the particles. Straight and staggered chain structures observed experimentally can be reproduced numerically in a multiple particle problem.