  A two-dimensional easy-plane ferromagnetic substrate, interacting with a
dipolar tip which is magnetised perpendicular with respect to the easy plane is
studied numerically by solving the Landau-Lifshitz Gilbert equation. The
dipolar tip stabilises a vortex structure which is dragged through the system
and dissipates energy. An analytical expression for the friction force in the
v$\rightarrow$0-limit based on the Thiele equation is presented. The
limitations of this result which predicts a diverging friction force in the
thermodynamic limit, are demonstrated by a study of the size dependence of the
friction force. While for small system sizes the dissipation depends
logarithmically on the system size, it saturates at a specific velocity
dependent value. This size can be regarded as an effective vortex size and it
is shown how this effective vortex size agrees with the infinite extension of a
vortex in the thermodynamic limit. A magnetic friction number is defined which
represents a general criterion for the validity of the Thiele equation and
quantifies the degree of nonlinearity in the response of a driven spin
configuration.
