Stanley Enemuo, Instructor at HeyTutor, Numerade Educator

18:29

University Physics with Modern Physics

Blood contains positive and negative ions and thus 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 $\textbf{Fig. E29.34}$.) (a) If the blood vessel is placed in a magnetic field $B$ perpendicular to the vessel, as in the figure, show that the motional potential difference induced across it is $\varepsilon = vBd$. (b) If you expect that the blood will be flowing at 15 cm/s for a vessel 5.0 mm in diameter, what strength of magnetic field will you need to produce a potential difference of 1.0 mV? (c) Show that the volume rate of flow ($R$) of the blood is equal to $R = \pi\varepsilon{d}/4B$. (Note: Although the method developed here is useful in measuring the rate of blood flow in a vessel, it is limited to use in surgery because measurement of the potential $\varepsilon$ must be made directly across the vessel.)

Chapter 29: Electromagnetic Induction

Section 4: Motional Electromotive Force