Final answer:
The Hall voltage induced on a patient's heart during an MRI scan with a wire simulating the conducting path on the heart wall, 7.50 cm long, moving at 10.0 cm/s in a 1.50-T magnetic field is 112.5 mV.
Step-by-step explanation:
To calculate the Hall voltage induced on a patient's heart while being scanned by an MRI unit, we can use the principle that the Hall voltage V_H is given by the formula V_H = B * l * v, where B is the magnetic field strength, l is the length of the conductor (or in this case, the simulated wire on the heart wall), and v is the velocity at which the conductor moves through the magnetic field.
In the given scenario, the conducting path is approximated by a wire 7.50 cm long moving at 10.0 cm/s perpendicular to a 1.50-T magnetic field. Therefore, the Hall voltage induced is:
\[V_H = 1.50 \, \text{T} \times 7.50 \times 10^{-2} \, \text{m} \times 10.0 \times 10^{-2} \, \text{m/s}\]
\[V_H = 1.50 \times 7.50 \times 10.0 \times 10^{-3} \, \text{V}\]
\[V_H = 0.1125 \, \text{V}\]
So, the Hall voltage induced on the patient's heart is 0.1125 V or 112.5 mV.