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 0.29 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 2.4 mm? V

Explanation / Answer

The magnetic field B = 0.25T the velocity of the blood v = 15cm/s (a) The force is felt by singly ionized ion               F = qvB sin here the velocity and magnetic field are perpendicular to each other so      F = qvB             = (1.6*10^-19C) ( 0.15m/s) (0.25T)             = 0.06 *10^-19 N or 6*10^-21 N (b) When the electric force due to electric field and magnetic force due to magnetic field are equal                then   qE = qv B                                                    E = vB = (0.15m/s) (0.25T)                               = 3.75*10^-2 N/C (c) When the artery diameter is d = 3.0mm        then the voltage   V = Ed                                      = (3.75*10^-2) (3*10^-3m)                                      = 11.25*10^-5 V                                      = 112.5 V

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