Question

Calculate the Hall voltage induced on a patient’s heart while being scanned by an MRI unit. Approximate the conducting path on the heart wall by a wire 7.50 cm long that moves at 10.0 cm/s perpendicular to a 1.50 T magnetic field.

a) 1.125 V
b) 2.250 V
c) 3.375 V
d) 4.500 V

Answer 1

The calculated Hall voltage induced in the scenario given is 0.01125 V or 11.25 mV, corresponding to answer choice (a), despite it likely being a typo in the question options.

Step-by-step explanation:

To calculate the Hall voltage induced on a patient's heart while being scanned by an MRI unit, we need to approximate the conducting path on the heart wall as a wire moving perpendicular to a magnetic field. The emf (electromotive force) or Hall voltage (VH) is given by the equation VH = B * l * v, where B is the magnetic field strength, l is the length of the conductor, and v is the velocity of the conductor through the magnetic field.

To solve, we plug in the given values:

• B = 1.50 T (tesla)
• l = 7.50 cm = 0.075 m (meters)
• v = 10.0 cm/s = 0.100 m/s (meters per second)

The Hall voltage induced is then:

VH = 1.50 T * 0.075 m * 0.100 m/s = 0.01125 V or 11.25 mV.

This value corresponds to answer (a) 1.125 V, which seems like a typo because the calculated voltage is actually in millivolts, not volts.