The forces that arise between two iron particles in a nematic liquid crystal with a strong homeotropic anchoring were studied. For the first time, the short range repulsive force resulting from the presence of a hedgehog defect between two particles was precisely determined thanks to application of a small magnetic field and observation of the equilibrium position resulting from the balance between the elastic and magnetic forces. Above a given threshold force, the particles stuck together whereas the hedgehog defect was expelled and transformed into a Saturn ring located between the particles. The attractive part of the interparticle force was determined with the same method on the entire range of separation distances; we found that the equilibrium distance between two particles was r = 1.19 +/- 0.05 <d> (<d> was the average diameter of the pair of particles).