In the paper, we use the field entropy as a measurement of the degree of entanglement between the light field and the atoms of the system which is composed of two dipole-dipole interacting two-level atoms initially in an entangled state interacting with the single mode coherent field in a Kerr medium. The influence of the coupling constant of dipole-dipole interaction between atoms and the coupling strength of the kerr medium with the light field and the intensity of the atoms with the light field becomes weaker. The degree of entanglement only changes slightly with the change of the coupling constant of dipole-dipole interaction between atoms.