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High energy photons from blazars can initiate electromagnetic pair cascadesinteracting with the extragalactic photon background. The charged component ofsuch cascades is deflected and delayed by extragalactic magnetic fields (EGMF),reducing thereby the observed point-like flux and leading potentially to multidegree images in the GeV energy range. We calculate the fluence of 1ES 0229+200as seen by Fermi-LAT for different EGMF profiles using a Monte Carlo simulationfor the cascade development. The non-observation of 1ES 0229+200 by Fermi-LATsuggests that the EGMF fills at least 60% of space with fields stronger than{\cal O}(10^{-16}-10^{-15})G for life times of TeV activity of {\calO}(10^2-10^4)yr. Thus the (non-) observation of GeV extensions around TeVblazars probes the EGMF in voids and puts strong constraints on the origin ofEGMFs: Either EGMFs were generated in a space filling manner (e.g.primordially) or EGMFs produced locally (e.g. by galaxies) have to beefficiently transported to fill a significant volume fraction, as e.g. bygalactic outflows.

Lower limit on the strength and filling factor of extragalactic magnetic fields