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 0.27 T to a coronary artery with a blood velocity of 13 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 3.5 mm?
V

Explanation / Answer

a) here the force on charge is Lorentz force = Electrical force + magnetic force

F = Eq + qVB

where E is electric field

q is charge

V is velocity

B is magnetic field

so here F = q V B

F = 1.6*10^-19 *0.13 *0.27

F = 5.61 e -21 N
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b) since Force F = Eq

Electric fied E = F/q

E = 5.61 e -21/1.6 e-19

E = 0.035 V/m or N/C

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c) Electric field and Electric potnetial are related by E = V/d

where d is the distance

so V = E d

V = 0.035 *3.5 e -3

V = 1.225 e -4 Volts

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