  We have estimated the magnetic field strengths of a sample of seven galaxies
using their non-thermal synchrotron radio emission at metre wavelengths, and
assuming energy equipartition between magnetic fields and cosmic ray particles.
Spatially resolved star formation rates (SFR) were estimated for the seven
galaxies along with five galaxies studied previously. For the combined sample
of twelve galaxies, the equipartition magnetic fields (B$_\textrm{eq}$) are
correlated with the SFR surface densities ($\Sigma_\textrm{SFR}$) at sub-kpc
scales with B$_\textrm{eq}$ $\propto$ $\Sigma_\textrm{SFR}^ {0.31\pm0.06}$,
consistent with model predictions. We estimated gas densities
($\rho_\textrm{gas}$) for a sub-sample of seven galaxies using archival
observations of the carbon monoxide (CO) rotational transitions and the atomic
hydrogen (HI) 21 cm line and studied the spatially-resolved correlation between
the magnetic fields and $\rho_\textrm{gas}$. Magnetic fields and gas densities
are found to be correlated at sub-kpc scale as B$_\textrm{eq}$ $\propto$
$\rho_\textrm{gas}^{0.40\pm0.09}$. This is broadly consistent with models,
which typically predict B $\propto$ $\rho_\textrm{gas}^{0.5}$.
