A sensor for sensing an angular position of an instrument relative to a static magnetic field includes a flexible beam, an electromagnetic device, and a measuring device. The beam at one end may be coupled to the instrument, and lies along a sensor axis when the beam is in a non -flexed state. The electromagnetic device is coupled to the beam and is configured for generating a magnetic sensor field aligned with the sensor axis. The measuring device communicates with the beam and is configured for measuring a property of the beam related to an amount of flexure of the beam. The sensor may be utilized to set the instrument at a desired angle prior to operating the instrument, and to determine whether the instrument has deviated from the desired angle during operation. The instrument may include a probe spinning module such as may be utilized in magnetic resonance experiments.