Answer to Question #91147 in Electricity and Magnetism for Matthew

Question #91147
To monitor the breathing of a patient in the hospital, a thin belt is wrapped around the patients chest. The belt is a composed of 200 turns. When the patient inhales, the area of the coil increases by 39 square centimeters. The magnitude of Earth's magnetic field is 50.0 μT and makes a 28 degree angle with the plane of the coil. If a patient takes 1.80 s to inhale, calculate the induced EMF generated in the coil during this time.
1
Expert's answer
2019-06-26T08:48:11-0400

First, write Faraday's law:


"emf=\\frac{d\\Phi}{dt}=\\frac{d(NBA\\space\\text{cos}\\space\\theta)}{dt}."

What changes here is the area if the coil, thus

"emf=NB\\space\\text{cos}\\space\\theta\\space\\frac{dA}{dt}=\\\\\n=200\\cdot50\\cdot10^{-6}\\cdot\\text{cos}\\space28^\\circ\\frac{39\\cdot10^{-4}}{1.80}=19.13\\cdot10^{-6}\\text{ V}."


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