  We present 850$\mu$m polarization observations of the L1689 molecular cloud,
part of the nearby Ophiuchus molecular cloud complex, taken with the POL-2
polarimeter on the James Clerk Maxwell Telescope (JCMT). We observe three
regions of L1689: the clump L1689N which houses the IRAS 16293-2422
protostellar system, the starless clump SMM-16, and the starless core L1689B.
We use the Davis-Chandrasekhar-Fermi method to estimate plane-of-sky field
strengths of $366\pm 55$ $\mu$G in L1689N, $284\pm 34$ $\mu$G in SMM-16, and
$72\pm 33$ $\mu$G in L1689B, for our fiducial value of dust opacity. These
values indicate that all three regions are likely to be magnetically
trans-critical with sub-Alfv\'{e}nic turbulence. In all three regions, the
inferred mean magnetic field direction is approximately perpendicular to the
local filament direction identified in $Herschel$ Space Telescope observations.
The core-scale field morphologies for L1689N and L1689B are consistent with the
cloud-scale field morphology measured by the $Planck$ Space Observatory,
suggesting that material can flow freely from large to small scales for these
sources. Based on these magnetic field measurements, we posit that accretion
from the cloud onto L1689N and L1689B may be magnetically regulated. However,
in SMM-16, the clump-scale field is nearly perpendicular to the field seen on
cloud scales by $Planck$, suggesting that it may be unable to efficiently
accrete further material from its surroundings.
