A heart surgeon can monitor the blood flow rate through an artery using an elect

Question

A heart surgeon can monitor the blood flow rate through an artery using an electromagnetic flowmeter. (See Figure 5). Electrodes A and B make contact with the outer walls of the blood vessel, which has a diameter of 1.8 mm. When a magnetic field of 0.027 T is applied by the poles of the magnet, an emf of 126 muV appears between the electrodes. Calculate the speed of the blood flowing in the vessel. In the diagram, electrode A is shown as positive, and electrode B is negative. Does this have to be the case, or could electrode A be negative? (In other words, does the sign of the emf depend on whether the charge carriers in the blood are predominantly positively or negatively charged?)

Explanation / Answer

(a)
B = 0.027 T
E = V/d
Where V is emf and d is distance btw the elctodes.
E = (126 * 10^-6)/(1.8 * 10^-3) V/m
E = 0.07 V/m

We know,
v = E/B
v = 0.07/0.027
v = 2.59 m/s
Speed of blood flowing in the vessel, v = 2.59 m/s

(b)
Using the right hand rule, the direction of the magnetic force exerted on the ions with a positive charge is upward while the force exerted on the negatively charged ions is downward. In both cases, the polarity of the electric field is consistent with the indicated potential of the electrodes. So the sign of emf does not depend on the charge of carriers !!

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