A patient is having a magnetic resonance imaging scan (an MRI) and has neglected

Question

A patient is having a magnetic resonance imaging scan (an MRI) and has neglected to remove a circular, metallic bracelet. The resistance of the bracelet is 0.0179 omega. The magnetic field within the MRI's solenoid is perpendicular to the opening of her bracelet. While taking the scan, the magnetic field decreases from 1.39 T o 0.45 Tin 1.10 seconds. If the magnitude of the average induced current in the bracelet during this time interval is 0.2503 A, what is the area of the opening of the circular bracelet? Tries 0/20

Explanation / Answer

From Farady's law, induced emf is given by

e = -d(phi)/dt

e = -d(BA)/dt = -AdB/dt = A(B1 - B2)/t

A = e t / (B1 - B2)

From Ohm's Law, e = IR = 0.2503 x 0.0179 = 0.0045 V

A = 0.0045 x 1.1 / (1.39 - 0.45) = 0.0053 m^2

Hence, A = 0.0053 m^2

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