Typical blood velocities in the coronary arteries range from 10 to 30 cm/s. An e

Question

Typical blood velocities in the coronary arteries range from 10 to 30 cm/s. An electromagnetic flowmeter applies a magnetic field of 0.23 T to a coronary artery with a blood velocity of 14 cm/s. As we can see in the figure below, this field exerts a force on ions in the blood, which will separate. The ions will separate until they make an electric field that exactly balances the magnetic force. This electric field produces a voltage that can be measured.

a. What force is felt by a singly ionized (positive) sodium ion?
N

b. Charges in the blood will separate until they produce an electric field that cancels this magnetic force. What will be the resulting electric field?
N/C

c. What voltage will this electric field produce across an artery with a diameter of 2.5 mm?
V

Explanation / Answer

magnetic field, B=0.23 T

blood velocity, v=14cm/sec

a)

F=q*v*B

F=(1.6*10^-19)*(14*10^-2)*0.23

F=5.15*10^-21 N

b)

electric force, F=q*E

5.15*10^-21=(1.6*10^-19)*E

===> E=3.22*10^-2 N/C

electric field, E=3.22*10^-2 N/C

c)

diameter, d=2.5mm

V=E*d

V=3.22*10^-2*(2.5*10^-3)

v=8.05*10^-5 v

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