Question

Mindy, a medical device engineer, is designing an apparatus to monitor the breathing of a patient. The apparatus consists of a stretchable loop of conductive material wrapped in a small band around the patient's chest. A constant uniform external magnetic field is produced by a nearby solenoid. As the patient inhales, his chest expands, stretching the chest band. The resulting increase in the area of the loop causes an emf to be induced in the loop. By measuring the induced emf, a device user can estimate the patient's breathing rate. Mindy needs the apparatus to be able to detect a change in area as small as 4.50 cm2 occuring over a time period of 1.50 s.

If the minimum emf that can be reliably detected is 3.00×10−4 V, what is the magnitude of the minimum external magnetic field that would be needed from the solenoid? magnitude of minimum external magnetic field: T

Due to practical constraints, the largest magnetic field that the solenoid can actually produce is 2.40×10−3 T. Mindy decides to compensate by using multiple loops of the conductive material in series. How many conductive loops should be in the chest band? minimum number of conductive loops:

Answer 1

The formula for EMF induced due to a magnetic flux is

where is the number of loops and

Since we are detecting a change in area in a given time and the magnetic field is held constant, we can re-write our equation as

First Case

Here, we have a single loop, and we need to find out the magnitude of the field to be used.

Note that in every calculation, I have used SI units to simplify it.

Putting in our values, we get...

The magnetic field required has a magnitude of one tesla.

Second case

Here, we have a limit on the magnetic field, and we need to find out .

A minimum of loops are required.