Chapter 21, Problem 25P

BO Measuring blood flow. Blood contains positive and negative ions and so is a conductor. A blood vessel therefore, can be viewed as an electrical wire. We can even picture the flowing blood as a series of parallel conducting slabs whose thickness is the diameter d of the vessel moving with speed v. (See Figure 21.59) (a) If the blood vessel is placed in a magnetic field $\stackrel{\to }{B}$ perpendicular to the vessel, as in the figure, show that the motional potential difference induced across it is ε = vBd. (b) If you expect that the blood will be flowing at 15 am/s for a vessel 5.0 mm in diameter what strength of magnetic field will you need in produce a potential difference of 1.0 mV? (c) Show that the volume rate of flow (R) of the blood is equal to R = πεd/4B. (Note: Although the method developed hers is useful in measuring the rate of blood flow in a vessel, it is of limited use in surgery because measurement of the potential ε must he made directly across the vessel.)

Figure 21.59

Problem 25.