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 0.0209 . 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 1.4 T to 0.47 T in 1.10 seconds. If the magnitude of the average induced current in the bracelet during this time interval is 0.1763 A, what is the area of the opening of the circular bracele

Explanation / Answer

Given

Resistance R = 0.0209 ohm

Initial magnetic field B1 = 1.4 T

Final magnetic field B2 = 0.47 T

Time interval t = 1.10 s

Current I = 0.1763 A

Solution

Emf produced in the bracelet V = IR

V = 0.1763 x 0.0209

V = 0.00368467 V

This emf is induced by the magnetic field

V = -NA(B2 – B1)cos/t

Here N = 1( number of turns in a coil) for the bracelet

Since the magnetic field is perpendicular to the bracelet the area vector and the magnetic field are parallel which means = 0o

V = - 1 x A x (0.47-1.4) x cos0 / 1.10

0.00368467 = A(0.8455)

A = 0.00436 m2

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