  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.
