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 accross the vessel. Suppose the speed of the blood is 0.34 m/s and the diameter of the vessel is 5.6 mm. In a 0.65 T magnetic field what is the magnitude of the voltage that is measured with the electrodes in the drawing?

To determine the magnitude of the voltage measured with the electrodes in the drawing, we can use the formula for electromagnetic induction. According to Faraday's Law, the induced voltage (V) is given by the equation:

V = B * l * v,

where:
- V is the induced voltage,
- B is the magnetic field strength,
- l is the length or distance across the vessel (the width of the blood flow perpendicular to the magnetic field),
- v is the velocity of the blood flow.

First, we need to convert the diameter of the vessel to its radius. The diameter is given as 5.6 mm, so the radius (r) can be calculated by dividing the diameter by 2:

r = 5.6 mm / 2 = 2.8 mm = 0.0028 m.

Next, we need to find the length (l) across the vessel. Since the blood flows perpendicularly with respect to the magnetic field, the length across the vessel is equal to its diameter (2r):

l = 2r = 2 * 0.0028 m = 0.0056 m.

Now, we can substitute the given values into the equation:

V = 0.65 T * 0.0056 m * 0.34 m/s.

By multiplying these values together, we find:

V = 0.0013624 V.

Therefore, the magnitude of the voltage measured with the electrodes is approximately 0.0013624 V.