University Physics with Modern Physics (14th Edition)

Published by Pearson
ISBN 10: 0321973615
ISBN 13: 978-0-32197-361-0

Chapter 29 - Electromagnetic Induction - Problems - Exercises - Page 984: 29.34

Answer

See explanation.

Work Step by Step

a. Each slab of flowing blood is like an object with maximum width d. It moves perpendicular to the field at speed v. $\epsilon=vBL$ becomes $\epsilon=vBd$. b. $B=\frac{\epsilon}{vd}=\frac{0.0010V}{(0.15m/s)(0.0050m)}=1.3T$ c. The blood vessel has a cross-sectional area of $\pi (d/2)^2$. The volume of blood that flows past a point in time t is $\frac{\pi d^2 vt}{4}$. The volume flow rate is volume/time. $$R=\frac{\pi d^2 vt}{4}\frac{1}{t}=\frac{\pi d^2 v}{4}$$ From before, $v=\frac{\epsilon}{Bd}$ $$R=\frac{\pi d^2}{4}\frac{\epsilon}{Bd}=\frac{\pi \epsilon d}{4B}$$
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