   Chapter 19, Problem 69AP

Chapter
Section
Textbook Problem

Using an electromagnetic flowmeter (Fig. P19.69), a heart surgeon monitors the flow rate of blood through an artery. Electrodes A and B make contact with the outer surface of the blood vessel, which has interior diameter 3.00 mm. (a) For a magnetic field magnitude of 0.040 0 T, a potential difference of 160 μV appears between the electrodes. Calculate the speed of the blood. (b) Verify that electrode A is positive, as shown. Does the sign of the emf depend on whether the mobile ions in the blood are predominantly positively or negatively charged? Explain. Figure P19.69

(a)

To determine
The speed of the blood.

Explanation

Given Info: The electromagnetic flow meter is used to monitor the flow rate of blood through an artery. Electrodes A and B are connected with the outer surface of the blood vessel with an inner diameter of 3.00mm . A potential difference of 160μV appears for a magnetic field of magnitude 0.0400T .

Explanation:

The direction of the magnetic field is from North Pole to the south pole of the magnet.

Because of the presence of the magnetic field the positive and the negative ions will experience force in different directions. The positive ions will get deflected towards the electrode A and the negative ions will get deflected towards electrode B . The separation of positive and negative ions will create the electric field which will be measured in the voltmeter.

When the system is in equilibrium the force due to ekectric field will be alanced by the magnetic force. In this condition,

qvB=qE       (1)

The electric field will be given as,

E=Vd       (2)

• V is the potential difference measured in the voltmeter
• d is the distance between the electrodes

From (1) and (2),

qvB=qVd

The velocity of the ions in turn the velocity of blood will be,

v=VBd

Substitute 160μV for V , 0

(b)

To determine
The electrode A is positive and whether the sign of the emf depend on whether the mobile ions in the blood are predominantly positive or negatively charged.

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