Question

Abdominal transducer belts are sometimes used in hospitals to monitor the breathing of patients. One particular model consists of a 200-turn coil of wire that wraps around a patient's chest. When the patient inhales, the area bounded by the coil increases by 46.0 cm². The magnitude of the Earth's magnetic field is 50.0 µT and makes an angle of 28.0° with the plane of the coil. If the patient takes 1.81 s to inhale, what is the magnitude of the average induced emf in the coil (in µV) during this time interval?

Answer 1

We know that magnitude of induced emf is given by:

Emf = N*d(phi)/dt

phi = magnetic flux = B.A = B*A*cos

EMF = N*d(B*A*cos )/dt = N*B*cos *dA/dt

A = change in area of loop = 46.0 cm^2 = 46.0*10^-4 m^2

dt = time interval = 1.81 sec

N = number of turns = 200 turns

B = magnetic field = 50.0*10^-6 T

= 90 - 28.0 = 62.0 deg

So,

EMF = 200*50.0*10^-6*46.0*10^-4*cos 62 deg/1.81

EMF = 11.93*10^-6 V

EMF = 11.93 V

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