Understanding the role of magnetic fields in star-forming regions is of fundamental importance. In the near future, the exceptional sensitivity of SKA will offer a unique opportunity to evaluate the magnetic field strength in molecular clouds and cloud cores through synchrotron emission observations. The most recent Voyager 1 data, together with Galactic synchrotron emission and Alpha Magnetic Spectrometer data, constrain the flux of interstellar cosmic-ray electrons between $approx3$ MeV and $approx832$ GeV, in particular in the energy range relevant for synchrotron emission in molecular cloud cores at SKA frequencies. Synchrotron radiation is entirely due to primary cosmic-ray electrons, the relativistic flux of secondary leptons being completely negligible. We explore the capability of SKA in detecting synchrotron emission in two starless molecular cloud cores in the southern hemisphere, B68 and FeSt 1-457, and we find that it will be possible to reach signal-to-noise ratios of the order of $2-23$ at the lowest frequencies observable by SKA ($60-218$ MHz) with one hour of integration.
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