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We show that weakly dissipating dielectric spheres made of materials such as glass, quartz, etc. can support high order Fano resonances associated with internal Mie modes. These resonances, happening for specific values of the size parameter, yield field-intensity enhancement factors on the order of 10⁴–10⁷, which can be directly obtained from analytical calculations. Associated to these “super-resonances”, we analyze the emergence of magnetic nanojets with giant magnetic fields, which might be attractive for many photonic applications.