An MRI technician moves his hand from a region of very low magnetic field streng

Question

An MRI technician moves his hand from a region of very low magnetic field strength into an MRI scanner's 1.60 T field with his fingers pointing in the direction of the field. His wedding ring has a diameter of 2.19 cm, and it takes 0.400 s to move it into the field. (a) What average current is induced in the ring if its resistance is 0.0100 ? (Enter the magnitude in amperes.) . A (b) What average power is dissipated (in W)? . W (c) What average magnetic field is induced at the center of the ring? (Enter the magnitude in teslas.) T (d) What is the direction of this induced magnetic field relative to the MRI's field? parallel antiparallel The magnitude is zero.

Explanation / Answer

The area of the ring is:

A = r² = x (0.011 m)² = 3.80 x 10^-4 m²

The change in magnetic flux is:

= BA = 1.60 T x (3.80 x 10^-4 m²) = 6.08 x 10^-4 Wb

The induced emf is:

|| = / t = (6.08 x 10^-4 Wb) / 0.400 s = 1.52 mV

Average current I = V/R = 1.52*10-3 / 0.0100 = 0.152 ampere

b) Average power

P = IV = 0.152*1.52*10-3 = 2.3104*10-4 W

c) B = uoI / 2r where uo = 4pi*10-7

So B = 4pi*10-7 * 0.152 / 2* 0.011 = 8.67*10-6 T

d) The  direction of this induced magnetic field relative to the MRI's fieldis parallel.

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