One way to use a magnetic field to detect whether a baby is breathing while asleep would be to set up a coil to generate a magnetic field. Another coil, a pickup coil, could be placed around the baby's chest . The baby's chest would expand and contract during breathing, changing the flux through the pickup coil, and that changing flux would induce a current which would be used to monitor the baby's breathing. Imagine that the generating coil produces a magnetic field with a strength of 0.01 T at the location of the sleeping baby. Treat the field as being perpendicular to the pickup coil (that is, the angle between the axis of the coil, or the normal, or the area vector, and the magnetic field is zero) for these calculations. The baby's chest can be approximated as a circle with a radius which varies from 9cm to 12 cm. (a) (15 pts) What is the magnetic flux through the pickup coil when the baby's chest is at its largest? What is that flux when the baby's chest is at its smallest?
(b) (10 pts) The baby takes 1.5 seconds to draw a full breath. (That is, breathing in takes 1.5 seconds. Breathing out would take another 1.5 seconds, but do not include that movement here.) What is the average rate of change in the magnetic flux during that time?
(c) (10 pts) If the coil around the baby has 10 loops and the effective resistance of the pickup coil is 50 ohms, what current will be seen by the detector?
(d) (5 pts) Describe the induced current - will it be constant, increase in a straight line, or vary sinusoidally? 5