You are designing an apparatus to monitor the breathing of a patient. The appara

Question

You are 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, you can estimate the patient's breathing rate. You want your apparatus to be able to detect a change in area as small as 4.50 cm^2 occuring over a time period of 1.50 s. If the minimum emf that can be reliably detected is 3.00 times 10^-4 V, what is the magnitude of the minimum external magnetic field that would be needed from the solenoid? Due to practical constraints, the largest magnetic field that the solenoid can actually produce is 2.40 times 10^-3 T. You decide to compensate by using multiple loops of the conductive material in series. How many conductive loops should be in the chest band?

Explanation / Answer

By Faraday’s law,

e = d/dt = d(BA)/dt = B*dA/dt

Plugging values,

3*10^-4 = B*(4.50*10^-4)/1.5    => B = 1.0 T

By Faraday’s law,

e = Nd/dt = d(BA)/dt = B*dA/dt

Plugging values,

3*10^-4 = N*2.40*10^-2*(4.50*10^-4)/1.5    => N= 42 loops

Related Questions

Navigate

• Browse (All)
• Browse Y
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.