  Charge fluctuations of a large quantum dot coupled to a two-dimensional lead
via a single-mode good Quantum Point Contact (QPC) and capacitively coupled to
a back-gate, are investigated in the presence of a parallel magnetic field. The
Zeeman term induces an asymmetry between transmission probabilities for the
spin-up and spin-down channels at the QPC, producing noticeable effects on the
quantization of the grain charge already at low magnetic fields. Performing a
quantitative analysis, I show that the capacitance between the gate and the
lead exhibits - instead of a logarithmic singularity - a reduced peak as a
function of gate voltage. Experimental applicability is discussed.
