Typical blood velocities in the coronary arteries range from

Typical blood velocities in the coronary arteries range from 10 to 30 cm/s. An electromagnetic flowmeter applies a magnetic field of 0.25 T to a coronary artery with a blood velocity of 15 cm/s. As we see in the figure, this field will exert 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.(Figure 1)

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

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

What voltage will this electric field produce across an artery with a diameter of 3 mm?

Express your answer using two significant figures.

Solution

a)

Charge of sodium ions

q=1.6*10^-19C

Magnetic force

F=qvB =(1.6*10^-19)*0.25*0.15

F=6*10^-21 N

b)

Electric field

E=F/q =6*10^-21/(1.6*10^-19)

E=0.0375 N/C

c)

Voltage

V=Ed =0.0375*(3*10^-3)

V=1.125*10^-4 Vots or 112.5 uV