For a given U(1)-bundle E over M = $\lambda _{2}$\{x1, ..., xn}, where the xi are n distinct points of $\lambda _{2}$, we minimise the U(1)-Higgs action and we make an asymptotic analysis of the minimizers when the coupling constant tends to infinity. We prove that the curvature (= magnetic field) converges to a limiting curvature that we give explicitely and which is singular along line vortices which connect the xi. This work is the three dimensional equivalent of previous works in dimension two (see [3] and [4]). The results presented here were announced in [12].