Chapter 21, Problem 74RPP

BIO Magnetic induction tomography (MIT) Magnetic induction tomography is an imaging method used in mineral, natural gas, oil, and groundwater exploration; as an archaeological tool; and for medical imaging MIT has also been used to measure topsoil depth in agricultural soils. Topsoil depth is information that many farmers need: for instance, corn yield is much higher in soil that has a deep topsoil layer above the underlying, impermeable claypan. Using a trailer attached to a tractor, a farmer can map an ${\text{80,000-m}}^{\text{2}}$

(about 20-acre) field for topsoil depth in about 1 hour.

Figure 21.28 shows how MIT works. A time-varying electric current in a source coil (Figure 21.28a) induces a changing magnetic field that passes into the region to be imaged—in this case, the soil (Figure 21.28b). This changing magnetic field induces a weak induced electric current in topsoil and a stronger induced current in the more conductive claypan soil at the same depth (Figure 21.28c; the current direction here is drawn as though the source current and source fields are increasing). This changing induced electric current in turn produces its own induced magnetic field (Figure 21.28d). The induced magnetic field passes out of the region being mapped to a detector coil (Figure 21.28e) near the source coil. The nature of the signal at the detector (its magnitude and phase) provides information about the region being mapped A strong signal returned to the detector coil indicates a claypan layer near the surface; a weak signal returns if the clay layer is deeper below the surface.

BIO Measuring the motion of flying insects Studying the motion of flying animals, particularly small insects, is difficult One method researchers use involves attaching a tiny coil with miniature electronics to the neck of an insect and another coil to its thorax (Figure 21.29). They place the insect in a strong magnetic field and observe the changing orientations and induced emfs of the two coils in the field as the insect flies Suppose that a 50-tum coil of radius $\text{2}\text{.0 }\times {\text{ 10}}^{\text{-3}}\text{m}$ is attached to a tsetse fly that is flying in a $\text{4}\text{.0 }\times {\text{ 10}}^{\text{- 3}}\text{-T}$ magnetic field The tsetse fly makes a $90°$ turn in 0.020 s. Consider the average magnitude of the induced emf that occurs due to the turn of the tsetse fly and its coil.

Which answer is closest to the magnitude of the flux change?

a. $1\times {10}^{-4}\text{T}\cdot {\text{m}}^{\text{2}}$

b. $2\times {10}^{-6}\text{T}\cdot {\text{m}}^{\text{2}}$

c. $3\times {10}^{-7}\text{T}\cdot {\text{m}}^{\text{2}}$

d. $5\times {10}^{-8}\text{T}\cdot {\text{m}}^{\text{2}}$