Question

You are working on an electromagnetic method for measuring the speed at which blood flows through arteries and veins inside the human body. Blood contains both positive and negative ions flowing together in the same direction. If those currents are exposed to a perpendicular magnetic field, they will be pushed in opposite directions, causing a charge separation between the two sides of the blood vessel. But the separated charges create an electric field that inhibits charge separation, so the effect is self-limiting. In equilibrium the net force (combined electric and magnetic) on ions in the blood will be zero, but there will be a measurable voltage across the blood vessel proportional to the electric field strength (this is called the Hall effect). (a) Draw a sketch showing how the magnetic field affects the paths followed by positive and negative ions. (b) Draw a force diagram for a positive or negative ion in equilibrium. (c) Derive a formula for how the blood speed v can be determined from measurements of the magnetic field strength, the voltage across the blood vessel, and the blood vessel diameter. (d) Determine the blood speed in the descending aorta, which has a diameter of 25mm, given that a 0.20T magnetic field produces a 2.5mV potential across the artery.

Answer 1