Mindy, a medical device engineer, is designing an apparatus to monitor the breathing of a patient. The apparatus consists of a stretchable loop of conductive material wrapped in a small band around the patient's chest. A constant uniform external magnetic field is produced by a nearby solenoid. As the patient inhales, his chest expands, stretching the chest band. The resulting increase in the area of the loop causes an emf to be induced in the loop. By measuring the induced emf, a device user can estimate the patient's breathing rate. Mindy needs the apparatus to be able to detect a change in area as small as 5.50 cm² occuring over a time period of 1.50 s. If the minimum emf that can be reliably detected is 3.00 × 10-4 V, what is the magnitude Bmin of the minimum external magnetic field that would be needed from Bmin = the solenoid? T Due to practical constraints, the largest magnetic field that the solenoid can actually produce is 3.50 × 10-3 T. Mindy decides to compensate by using multiple loops of the conductive material in series. What is the minimum number Nmin of wire loops that will allow the chest band to function as desired? Enter the smallest integer value. Nmin = loops

Mindy, a medical device engineer, is designing an apparatus to monitor the breathing of a patient. The apparatus consists of a stretchable loop of conductive material wrapped in a small band around the patient's chest. A constant uniform external magnetic field is produced by a nearby solenoid. As the patient inhales, his chest expands, stretching the chest band. The resulting increase in the area of the loop causes an emf to be induced in the loop. By measuring the induced emf, a device user can estimate the patient's breathing rate. Mindy needs the apparatus to be able to detect a change in area as small as 5.50 cm² occuring over a time period of 1.50 s. If the minimum emf that can be reliably detected is 3.00 × 10-4 V, what is the magnitude Bmin of the minimum external magnetic field that would be needed from Bmin = the solenoid? T Due to practical constraints, the largest magnetic field that the solenoid can actually produce is 3.50 × 10-3 T. Mindy decides to compensate by using multiple loops of the conductive material in series. What is the minimum number Nmin of wire loops that will allow the chest band to function as desired? Enter the smallest integer value. Nmin = loops

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter23: Faraday’s Law And Inductance

Section: Chapter Questions

Problem 5P

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Figure P30.39 shows a stationary conductor whose shape is similar to the letter e. The radius of its circular portion is a = 50.0 cm. It is placed in a constant magnetic field of 0.500 T directed out of the page. A straight conducting rod, 50.0 cm long, is pivoted about point O and rotates with a constant angular speed of 2.00 rad/s. (a) Determine the induced emf in the loop POQ. Note that the area of the loop is a2/2. (b) If all the conducting material has a resistance per length of 5.00 /m, what is the induced current in the loop POQ at the instant 0.250 s after point P passes point Q? Figure P30.39