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A VLA Sky Survey of the extragalactic sky at S band (2-4 GHz) withpolarization information can uniquely probe the magneto-ionic medium in a widerange of astrophysical environments over cosmic time. For a shallow all-skysurvey, we expect to detect over 4 million sources in total intensity $>$ 0.45mJy beam$^{-1}$ and over 2.2$\times$10$^5$ sources in polarized intensity. Withthese new observations, we expect to discover new classes of polarized radiosources in very turbulent astrophysical environments and those with extremevalues of Faraday depth. Moreover, by determining reliable Faraday depths andby modeling depolarization effects, we can derive properties of themagneto-ionic medium associated with AGNs, absorption line systems andgalaxies, addressing the following unresolved questions: (1) What is thecovering fraction, the degree of turbulence and the origin of absorption linesystems? (2) What is the thermal content in AGNs and radio galaxies? (3) How doAGNs and galaxies evolve over cosmic time? (4) What causes the increase inpercentage polarization with decreasing flux densities at the low flux densityend of the polarized source count? (5) What is the growth rate of large-scalemagnetic fields in galaxies?

A Wideband Polarization Survey of the Extragalactic Sky at 2-4 GHz: A Science White Paper for the VLA Sky Survey