  The critical current density of a superconducting film can be easily
determined by an inductive and contactless method. Driving a sinusoidal current
in a single coil placed in front of a superconducting sample, a non zero third
harmonic voltage V_3 is induced in it when the sample goes beyond the Bean
critical state. The onset of V_3 marks the value of current beyond which the
sample response to the magnetic induction is no more linear. To take into
account, in a realistic way, the magnetic coupling between the film and the
coil we have developed a discrete model of the inducing and induced currents
distribution. In the framework of this model the magnetic field profile on the
sample surface and the coefficient linking the current flowing in the coil and
the critical current density J_C of superconducting thin films is evaluated.
The numerical results are checked measuring J_C of several thin films of
YBa_2Cu_3O_(7-d) of known superconducting properties, used as a control
material.
