An apparatus for measuring a magnetic field is described, which comprises a core and an exciter coil for remagnetizing the core material. The remagnetizable core material is embodied as a layer or as multiple layers disposed at a distance from one another, and the core has a maximum total extension G where 2.5 mm≧G≧0.2 mm, a ratio of length to width that is greater than or equal to a value of twenty, and a thickness D where 2 μm≧D≧0.2 μm. Also described is a corresponding method for measuring a magnetic field.