Using relationship of the quasi-static index of refractive εeffμeff and the static one εeff in granular film dielectric, the index of refractive of photonic crystal were calculated in the low-frequency limit. The calculation indicates that, due to the eddy current (or the polarized current) induced by the low-frequency waves, the non-magnetic photonic crystal appears the diamagnetic resonance, which depends on the relationship between the radius of the cylinder a and skin deep δ0. If δ0a, the inside electromagnetic field of the inclusion is concealed. Each inclusion behaves like the ideal diamagnetic with μ=0. The diamagnetic permeability of (H polarization wave) photon crystal is linearly reduced with the increase of the filling fractions (μeff=1－f ). On the contrary, when skin layer is larger than the radius, the diamagnetic resonance can be neglected. The magnetization of the periodicity particle composite media induces distinct values of the quasistatic and static indices of refraction, which explains a paradox with noncommuting limits.