worder to monitor the breathing of a patient, 250 stretchable loops of conductiv
ID: 2031111 • Letter: W
Question
worder to monitor the breathing of a patient, 250 stretchable loops of conductive material are wrapped in a small band around the patient's chest. As the patient inhales, his chest expands, stretching the chest band. In the presence of a constant uniform magnetic field produced by a nearby solenoid, this resulting change in the area of the loop results in an induced emf. Thus, by measuring the induced emf in the loop, you can measure the patient's breathing rate. This apparatus must be able to detect a change in area as small as 5.50 cm2 occuring over a time period of 1.75 s, but the smallest emf that can be reliably detected is 3.00 x104 V. Given these constraints, what is the magnitude of the minimum magnetic field that would be needed from the solenoid? Minimum solenoid magnetic field NumberExplanation / Answer
Given,
N = 250 ; A = 5.5 cm^2 ; t = 1.75 s emf = 3 x 10^-4 V ;
We know that the induced emf is given by:
emf = N -d(phi)/dt
emf = N B (dA/dt)
B = emf/(dA/dt)
dA/dt = 5.5 x 10^-4/1.75 = 3.14 x 10^-4 m^2/s
B = 3 x 10^-4/250 x 3.14 x 10^-4 = 4.2 x 10^-3 T
Hence, B = 4.2 x 10^-3 T
for a single loop
B = 3 x 10^-4/3.14 x 10^-4 = 0.96 T
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