Answer to Question #91147 in Electricity and Magnetism for Matthew

Question

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.

Answer 1

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

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