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 produced by a nearby solenoid. As the patient inhales, his chest expends, 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 change in area as small as 5.50 cm^2 occurring over a time period of 1.50 s. If the minimum emf that can be reliably detected is 2.00 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 3.50 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

part A:

magnitude of induced emf=change in magnetic flux linkage/time duration

=magnetic field*change in area/time duration

==>2*10^(-4)=magnetic field*5.5*10^(-4)/1.5

==>magnetic field=2*10^(-4)*1.5/(5.5*10^(-4))=0.54545 T

part B:

let number of loops be N.

then N*magnetic field *change in area/time duration=emf induced

==>N*3.5*10^(-3)*5.5*10^(-4)/1.5=2*10^(-4)

==>N=2*10^(-4)*1.5/(3.5*5.5*10^(-7))=155.84

so number of turns required 156. (nearest integer)

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