A robotic surgical system comprising a surgical instrument. The surgical instrument includes an elongate, hollow shaft having a proximal end, a distal end, and a flexible section. The surgical instrument also includes a sensor apparatus comprising an electromagnetic sensor. The robotic surgical system also includes a force transmission mechanism coupled to the proximal end of the shaft and a processor communicatively coupled to at least the sensor apparatus. The processor is configured to receive sensor data from the sensor apparatus and to use the sensor data with mechanical property data for the surgical instrument and material property data for the surgical instrument to determine external force information for the surgical instrument.