  The Copenhagen problem where the primaries of equal masses are magnetic
dipoles is used in order to determine the Newton-Raphson basins of attraction
associated with the equilibrium points. The parametric variation of the
position as well as of the stability of the Lagrange points are monitored when
the value of the ratio $\lambda$ of the magnetic moments varies in predefined
intervals. The regions on the configuration $(x,y)$ plane occupied by the
basins of convergence are revealed using the multivariate version of the
Newton-Raphson iterative scheme. The correlations between the basins of
attraction of the libration points and the corresponding number of iterations
needed for obtaining the desired accuracy are also illustrated. We perform a
thorough and systematic numerical investigation by demonstrating how the
dynamical quantity $\lambda$ influences the shape, the geometry and also the
degree of fractality of the attracting domains. Our numerical results strongly
indicate that the ratio $\lambda$ is indeed a very influential parameter in the
electromagnetic binary system.
