  Our understanding of planetary dynamos and liquid cores relies on the
existence of a Tangent Cylinder (TC). This imaginary surface that physically
separates polar and equatorial regions stems from Taylor-Proudman's Constraint
(TPC) due to planetary rotation only. Here we establish mathematically and
verify experimentally that a magnetic field aligned with the rotation incurs a
flow \emph{into} the TC, linked to the flow along it by a \emph{magnetic} TPC.
This constraint sheds new light on flows in planetary cores and flows subject
to both magnetic fields and rotation in general.
