  Magnetic perturbations on ground at high latitudes are directly associated
only with the divergence-free component of the height-integrated horizontal
ionospheric current, $\textbf{J}_{\perp,df}$. Here we show how
$\textbf{J}_{\perp,df}$ can be expressed as the total horizontal current
$\textbf{J}_\perp$ minus its curl-free component, the latter being completely
determined by the global Birkeland current pattern. Thus in regions where
$\textbf{J}_\perp = 0$, the global Birkeland current distribution alone
determines the local magnetic perturbation. We show with observations from
ground and space that in the polar cap, the ground magnetic field perturbations
tend to align with the Birkeland current contribution in darkness but not in
sunlight. We also show that in sunlight, the magnetic perturbations are
typically such that the equivalent overhead current is anti-parallel to the
convection, indicating that the Hall current system dominates. Thus the ground
magnetic field in the polar cap relates to different current systems in
sunlight and in darkness.
