Effects of uniform magnetic fields on the interaction and coalescence of side-by-side rising bubbles of dielectric fluids were not studied; so in the present research, effects of different strengths of uniform magnetic field on the interaction of two bubbles rising side by side in a viscous and initially stagnant liquid are studied, numerically. For numerical modeling of the problem, a full computer code was developed to solve the governing equations which are continuity, Navier-Stokes, magnetic field and interface capturing equations which are level set and re-initialization equations. The finite volume method is used for the discretization of the hydrodynamic equations where the finite difference method is used to discretization of the magnetic field equations. The results are compared with available numerical and experimental results which show a good agreement. It is found that the uniform magnetic field can be used for contactless control of side-by-side coalescence of bubbles.