In medicine, it is often important to monitor the blood flow in certain areas of

Question

In medicine, it is often important to monitor the blood flow in certain areas of the body. However, the movement of blood is difficult to monitor directly. Instead, some medical devices use the Hall Effect, taking advantage of the fact that the blood flowing through a vein contains a considerable amount of free ions. As a simplification, we consider the vein in a patient's arm to be of rectangular cross-section, as shown above, with the width of the vein at w = 4.00 mm and height h = 2.65 mm. The entire section of the vein is immersed in a constant magnetic field of 0.0955 tesla pointing horizontally. The equipment (not shown) constantly monitors the resulting Hall voltage. Suppose medical precautions mandate that the speed of the blood flow for this particular component of the body should never drop below 21.90 cm/s.^* At what minimum Hall voltage (in millivolts) should you design the medical device to trigger an alarm to the medical staff?

Explanation / Answer

w = 4mm ,h =2.65mm, drift velocity vd = 21.9 cm/s , B = 0.0955 T

Hall voltage VH = vd*w*B = 0.219*0.00265*0.0955

VH = 0.0554 mV

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