To monitor the breathing of a hospital patient, a thin belt is girded around the

Question

To monitor the breathing of a hospital patient, a thin belt is girded around the patient's chest as in the figure below. The belt is a 195-turn coil. When the patient inhales, the area encircled by the coil increases by 44.0 cm2. The magnitude of Earth's magnetic field is 50.0 ?T and makes an angle of 29.0° with the plane of the coil. Assuming a patient takes 1.90 s to inhale, find the magnitude of the average induced emf in the coil during that time.

(Answer is in ?V)

Please explain your answer legibly and step by step .

Explanation / Answer

Avg Induced EMF is given by:

Emf = -N*d(phi)/dt

phi = magnetic flux = B*A*cos theta

Emf = -N*B*cos theta*dA/dt

N = 195 turn

B = 50*10^-6 T

dA = 44 cm^2 = 44*10^-4 m^2

dt = 1.90 sec

theta = 90 - 29 = 61 deg (Since we need angle perpendicular to the surface of coil)

So

EMF = -195*50*10^-6*44*10^-4*(cos 61 deg)/1.90

EMF = -1.095*10^-5 V

|EMF| = 10.95 uV

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