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.)

## Discussion

## Video Transcript

So we're given the circuit that is shown in 29.31 And for part, they were asked to find the induced. Whether or not the induced current is clockwise or counterclockwise. Well, the induced current is going to be acting to resist the change in the force. So using the right hand rule where the, uh, the magnetic field's coming out of the page, the velocity of the magnets to the right, using that curl that's going to be clockwise. So it's gotta be counterclockwise to reduced resist that induced change. So for part A, we can just type out here counterclockwise, okay and then for Part B and asked us to calculate the velocity, given the information of resistance, the power of a 0.84 jewels per second, the magnetic field in the length of the rod. So a lot. The voltage is equal to the velocity times a magnetic field times the length of the rod. Therefore, velocity is equal to voltage, divided by magnetic field times the length of the rod Well, power here is equal to voltage squared, divided by resistance. Therefore, voltage is equal to the square root of power times resistance. So playing that in we have a square root of power times resistance divided by magnetic field times linked to the rod. We know all those values, so plugging them into the expression, we find that the velocity is equal to 26 0.3 meters for a second weaken box set in as our solution for part B.

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