Proximity effect misunderstanding
I do not understand why the eddy current are not maximum at the place
  where the magnetic fields is maximum


They are, but....

An eddy current will circulate current in each parallel strip therefore, an eddy current neither adds-to nor diminishes the main current flow in the plate. That main current flow still occupies that part of the plate that has the least inductance and actually, the eddy currents will diminish that inductance a little.


  Hence if the eddy current is maximum at this place, the eddy current
  being opposed to the current flowing into the conductor, the current
  should be lower at the place where the magnetic field is maximum


No, it neither detracts nor enhances the main current because it is an eddy and eddies circulate.