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Measuring blood flow. Blood contains positive and negative ions and therefore 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 $21.62 . )$ (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 $\mathcal{E}=v B d .$ (b) If you expect that the blood will be flowing at 15 $\mathrm{cm} / \mathrm{s}$ for a vessel 5.0 $\mathrm{mm}$ in diameter, what strength of magnetic field will you need to produce a potential difference of 1.0 $\mathrm{mV} ?$ (c) Show that the volume rate of flow $(R)$ of theblood is equal to $R=\pi \mathcal{E} d / 4 B .$ (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 $\mathcal{E}$ must be made directly across the vessel.)

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a. the potential difference between the ends is $[\overrightarrow{v B d}]$b. the magnetic field is $[1.34 \mathrm{T}]$c. the volume rate of flow is $\left[\frac{\pi d \varepsilon}{4 B}\right)$

Physics 102 Electricity and Magnetism

Chapter 21

Electromagnetic Induction

Current, Resistance, and Electromotive Force

Direct-Current Circuits

Magnetic Field and Magnetic Forces

Sources of Magnetic field

Inductance

Alternating Current

Rutgers, The State University of New Jersey

Simon Fraser University

University of Sheffield

Lectures

03:27

Electromagnetic induction is the production of an electromotive force (emf) across a conductor due to its dynamic interaction with a magnetic field. Michael Faraday is generally credited with the discovery of electromagnetic induction in 1831.

08:42

In physics, a magnetic field is a vector field that describes the magnetic influence of electric currents and magnetic materials. The magnetic field at any given point is specified by both a direction and a magnitude (or strength); as such it is a vector field. The term is used for two distinct but closely related fields denoted by the symbols B and H, where H is measured in units of amperes per meter (usually in the cgs system of units) and B is measured in teslas (SI units).

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Measuring blood flow. Bloo…

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Measuring Blood Flow. Bloo…

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BIO Measuring Blood Flow. …

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BIO Measuring blood flow. …

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Blood contains positive an…

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Blood-flow meter. Blood pl…

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One way to measure blood f…

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An electromagnetic flowmet…

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Consider a blood-flow sens…

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The flow of blood in a blo…

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So for party, we can say each slab of flowing blood has a maximum with D, so given that they have a maximum with D and it is moving again, moving blood is moving perpendicular to the field with speed V. We can say that the induced EMF is going to be equal to BBO. However, L now equals D. So this would be equal to B B times. So that would how that's how we would applied this. The IMF formula for this blood vessel now for part B when they're asking for the magnitude of the magnetic field, this is going to be equal to the IMF, divided by the velocity of the blood divided by the width of the of the of the slab or that with of the blood vessel in this case. So this would be equal Tio one times 10 to the negative third votes, divided by 0.15 meters per second and then times thie with of five times 10 to the negative third meters. And so this is equaling 1.3 Tesla's. So this would be your answer for a party and now for part. See, however, we need to find the what would be the R would be the essentially the the volume flow rate. So we can say that for the blood vessel Oh, the blood vessel has a cross sectional area, eh? And this is going to simply be good to pi r squared. Or we can say pie D squared over four. So if we were to plug in D over two for the diameter, divided by two for the radius, we know that the volume of blood, yeah, passing through Ah a the cross sectional area of vessel In time t we can create an equation and say pie d squared Time's vt divided by four. So that would be the volume of the blood passing through the cross sectional area were simply multiplying the cross sectional area by a velocity. So I would give us meteors cubed per second and then times the time, which would be in second so that the just meters cute. So I would be the volume. And then if we wanted a volume flow rate, this would be equal to volume divided by time, of course. And this we can say that we can denote this are this would be equal to pi d squared V over four. So we would eliminate t. Essentially, we know that V is going to be equal to the Absalon the IMF divided by the magnitude of the magnetic field times thie with of the blood vessel. So we can say that our is going to be equal to pi d squared, divided by four. And then times he over b d. This is going to be equal to pie. Me, Absalon Mother, why absolutely d divided by four b bye bye for media. It's actually the only thing I cancelled out is this Cancel out with one of these and that's about it. So this would be equal to our and we've to find our as the volume flow rate. So this would be the volume florrie, that is the end of the solution. Thank you for watching

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