A magnetic sensor device having a first magnetic core structure which is aligned along a first central longitudinal axis and has at least one first coil, and having a second magnetic core structure which includes at least one second coil, the second magnetic core structure extending from a first end face of the second magnetic core structure along a second central longitudinal axis to a second end face of the second magnetic core structure, the second central longitudinal axis lying in a plane aligned in a direction normal to the first central longitudinal axis, and the second magnetic core structure being positioned in relation to the first magnetic core structure in such a way that a clearance between the first end face of the second magnetic core structure and a first center of mass of the first magnetic core structure is less than 20% of a maximum extension of the first magnetic core structure along the first central longitudinal axis.