Frustrated by the small Hall voltage obtained in blood flow measurements, a medical physicist decides to increase the applied magnetic field strength to get a 0.500-V output for blood moving at 30.0 cm/s in a 1.50-cm-diameter vessel. (a) What magnetic field strength is needed? (b) What is unreasonable about this result? (c) Which premise is responsible?

Video Transcript

This is College Physics Answers with Shaun Dychko. A hypothetical Hall voltage of 0.500 volts is wanted when there's blood moving at 30.0 centimeters per second, which is 30.0 times 10 to the minus 2 meters per second, and in a blood vessel with a diameter of 1.50 centimeters, which is 1.50 times 10 to the minus 2 meters. So the Hall voltage is the magnetic field strength multiplied by the distance across the thing that's having its Hall voltage— in this case, it's a cylindrical blood vessel with a diameter d— multiplied by the speed of the fluid moving in it or the charge carriers moving in it. So we divide both sides by diameter and speed to solve for B and so the magnetic field strength then is Hall voltage divided by diameter times speed. So that's 0.500 volts divided by 1.50 times 10 to the minus 2 meters times 30.0 times 10 to the minus 2 meters per second which is 111 tesla. And by the way, blood counts as a moving charge carrier only because it will have ions in it like most natural water will; if you had like perfectly pure distilled water with no dissolved ions in it then it would not create a Hall voltage because there would be no charges to separate. So this magnetic field strength of 111 tesla is far greater than what's possible with laboratory technology... you know, with superconducting coils and so on and really high currents, you can get on the order of 2.0 tesla maybe in an MRI machine. Well, 111 tesla is not realistic so the expected Hall voltage is too high.