To monitor the breathing of a hospital patient a thin belt i

To monitor the breathing of a hospital patient, a thin belt is girded around the patient\'s chest. The belt is a 200-turn coil. When the patient inhales, the area encircled by the coil increases by 47.0 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. Assuming a patient takes 1.90 s to inhale, find the magnitude of the average induced emf in the coil during this time interval. Answer in terms of µV

Solution

Emf = -N*d(phi)/dt

phi = B*A*cos X

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

Angle between magnetic field and direction of area with normal is 90 - 28 = 62 deg

Emf = -200*50*10^-6*cos 62 deg*[47*10^-4/1.9]

Emf = -11.61 uV