The invention relates to a flow rate sensor (10), which is designed to measure an electrically conductive fluid that flows in pipework. Said sensor comprises a measuring tube (11), which can be inserted into the run of pipework to conduct the fluid, said measuring tube (11) being electrically non-conductive on at least one inner face that comes into contact with the fluid, an electrode assembly (14) comprising at least two measuring electrodes that are located on the measuring tube and tap an electric voltage that is induced in the fluid, in addition to a magnetic field system that is also located on the measuring tube (11). The magnetic field system of the inventive flow rate sensor is equipped with at least two saddle-shaped field coils (15, 16), for generating a magnetic field that penetrates the fluid when operational, a respective ferromagnetic pole shoe (21, 22) for the field coils, for conducting the magnetic field towards the fluid and at least one ferromagnetic feedback element running around the measuring tube upstream of the two field coils and at least one ferromagnetic feedback element (23, 24) running around the measuring tube downstream of the two field coils, for conducting the magnetic field around said measuring tube. The pole shoes are magnetically coupled to the feedback elements by means of respective ferromagnetic coupling elements (17, 18, 19, 20). Each of said coupling elements, which are preferably configured in a standard manner, comprises at least one substantially gully-type cover segment (17a, 18a, 19a, 20a), which receives a first winding section of the respective field coil, said section essentially lying on a first circumferential segment of the measuring tube, or a second winding section (15a, 15b) of the respective field coil, said section essentially lying on a second circumferential segment of the measuring tube.