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 = 3.45 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 24.80 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

Basically, we need to find the Hall Voltage VH when the speed v is 24.8 cm/s

Hall voltage is given by VH = IB/new

But current I is given by the following way

n is the charge density (no of charges per unit volume)

cross sectional area x velocity gives volume of blood crossing a section per second = wh x v

Charge density x volume crossing per second = no of charges crossing per second

n x wh x v = no of charges crossing per second

no of charges crossing per second x charge of each particle = charge crossing per second

nwhv x e = charge / second which is nothing bit the current

therefore I = nwhve

substituting in VH = IB/new

VH = (nwhve)B/new

VH = hvB

VH = 3.45x 10-3 x 24.8 x 10-2 x 0.0955 = 8.17098 x 10-5 V

Therefore, alarm should be triggered at 0.0817 mV

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.