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?

The magnitude of the voltage that is measured with the electrodes in the drawing is 0.0014 V.

To calculate the magnitude of the voltage measured with the electrodes in the drawing, we can use the equation given by the Hall effect:

V = B * v * d * E

Where:
V is the voltage measured (unknown)
B is the magnetic field strength (0.65 T)
v is the speed of the blood (0.34 m/s)
d is the diameter of the vessel (5.6 mm = 0.0056 m)
E is the electric field (unknown)

Since we are given the speed of the blood and the magnetic field strength, we can proceed to calculate the magnitude of the voltage.

V = (0.65 T) * (0.34 m/s) * (0.0056 m) * E

To find E, we need to consider the properties of the blood as a conductor. Since the blood is conductive enough, we can assume it has a reasonable electrical conductivity. For this example, we'll assume a typical value for the electrical conductivity of blood, which is approximately 0.6 S/m.

Substituting this value into the equation:

V = (0.65 T) * (0.34 m/s) * (0.0056 m) * (0.6 S/m)

Now, let's calculate the magnitude of the voltage:

V = 0.0065136 V

Therefore, the magnitude of the voltage measured with the electrodes in the drawing is approximately 0.0065136 V.

To calculate the magnitude of the voltage measured by the electrodes in the given scenario, we can use the equation for the electromotive force (EMF) induced in a conductor moving perpendicular to a magnetic field. The equation is given by:

EMF = B * v * d

Where:
EMF = Electromotive force (voltage)
B = Magnetic field strength (Tesla)
v = Velocity of the conductor (m/s)
d = Length of the conductor (m)

In this case, the diameter of the vessel is given, so we need to calculate the length of the conductor. The length of the conductor can be found using the formula for the circumference of a circle:

Circumference = π * Diameter

Substituting the given values:

Circumference = π * 5.6 mm = 3.14 * 0.0056 m ≈ 0.0176 m

Now we can calculate the EMF:

EMF = 0.65 T * 0.34 m/s * 0.0176 m

Calculating this expression will give us the magnitude of the voltage measured by the electrodes.