We know that magnetic fields are pervasive across all scales in the Universe and over all of cosmic time and yet our understanding of many of the properties of magnetic fields is still limited. We do not yet know when, where or how the first magnetic fields in the Universe were formed, nor do we fully understand their role in fundamental processes such as galaxy formation or cosmic ray acceleration or how they influence the evolution of astrophysical objects. The greatest challenge to addressing these issues has been a lack of deep, broad bandwidth polarimetric data over large areas of the sky. The Square Kilometre Array will radically improve this situation via an all-sky polarisation survey that delivers both high quality polarisation imaging in combination with observations of 7-14 million extragalactic rotation measures. Here we summarise how this survey will improve our understanding of a range of astrophysical phenomena on scales from individual Galactic objects to the cosmic web.
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