Blood contains positive and negative ions and thus is a...

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.)

Transcript

00:03 So in this problem for part a, we know the thickness of a vessel is given by d.

00:14 So d represents the thickness of your vessel.

00:59 We know speed is v.

01:06 And again, we just write in what you do know, given the problem.

01:15 So we understand when placed, when the vessel is placed in the, magnetic field, there's a force that image from that position where the vector is placed.

01:33 And the force is represented by f.

01:45 The force that emits from the electric field, fb, f sub b is equal to the charge q times the speed b, times the magnetic field, b.

02:08 This force, it causes the charge to move.

02:14 And when the charge moves, there is a creation of an excess charge at both upper and lower end, which in turn creates an electric field.

02:28 That's where we have f -tub -e.

02:31 F -sub -e, is equal to the charge that is being created times the electric field.

02:54 That's the force that creates the electric field.

03:01 This charges are in equilibrium.

03:05 So q sub e, the charges, so during the state of rest, equilibrium.

03:51 So qe is equal to the charge times the speed times the electric field.

04:03 Where it's just alpha e, the electric field becomes bb.

04:26 The potential difference between the upper end and the lower end using this equation you can find v is equal to ed again d being the thickness and e being the electric field and let's call this equation one now we're going to substitute equation one for the value of e substitute substitute for e and we're going to we're going to we rewrite e as epsilon as the greek value epsilon.

06:10 So epsilon so this is how you write epsilon and for big so if you rewriting this so what's been a 72e which is zb so epsilon becomes the potential difference v times the field times your thickness so that's for your part a epsilon is equal to the potential difference times the magnetic field times the thick for part b they want to say if you expect if i am and if you expect that the blood will be flowing what is the strength of the magnetic field so the action for the strength of the magnetic field given that it produces a potential difference of one and v so they give it was the potential difference tv, you know, speed given the symbol is v.

09:06 And we're, we told the speed is 15 centimeters per second, converting 15 centimeters per second, we have 0 .15 meters per second.

09:31 We're given the thickness in this problem to be b diameter is equal to 5 .0 millimeters converning that to meters we have 5 .0 times 10 to negative 3 meters to find the emotional electromotive force, emv, emf, i'm sorry...

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