The drawing shows a type of flow meter that can be used to measure the speed of

Question

The drawing shows a type of flow meter that can be used to measure the speed of blood in situations when a blood vessel is sufficiently exposed (e.g., during surgery). Blood is conductive enough that it can be treated as a moving conductor. When it flows perpendicularly with respect to a magnetic field, as in the drawing, electrodes can be used to measure the small voltage that develops across the vessel. Suppose the speed of the blood is 0.35 m/s and the diameter of the vessel is 8.2 mm. In a 0.47-T magnetic field what is the magnitude of the voltage that is measured with the electrodes in the drawing? Please include units. Thank you!

Explanation / Answer

We know that the magnetic force on moving charge is given by:

Fm = q v B

electric force on a charge is:

Fe = q E

these two balances each other so

Fm = Fe

q v B = q E

E = v B = 0.35 x 0.47 = 0.165 V/m or N/C

We know that,

E = V/d => V = E d

V = 0.165 V/m x 8.2 x 10^-3 m = 1.35 x 10^-3 Volts

Hence, V = 1.35 x 10^-3 Volts = 1.35 milliVolts

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