An MRI technician moves his hand from a region of very low magnetic field strength into an MRI scanner’s 2.00 T field with his fingers pointing in the direction of the field. Find the average emf induced in his wedding ring, given its diameter is 2.20 cm and assuming it takes 0.250 s to move it into the field. (b) Discuss whether this current would significantly change the temperature of the ring.

Explanation:

Using Len's and Faraday formula

Faraday law states that a voltage is induced in a circuit whenever relative motion exists between a conductor and a magnetic field and that the magnitude of this voltage is proportional to the rate of change of the lux

Lenz law states that the direction of an induced emf is such that it will always opposes the change causing it

induce emf, e = -NΔФ/Δt

where Ф = BAcosФ and Ф = 0

N = number of turns, 1

B = 2 T

d = 2.20 cm = 0.022 m

radius = 0.022 m / 2 = 0.011 m

A area = πr² = 3.142 ( 0.011)² = 0.000380 m²

e = ( 0.00038 m²) ( 2 / 0.250 s) = 0.00304 V

b) Using ohm's law e = IR

since the the ring will be a metal e.g silver, and metals are good conductors of electricity, the resistances will be very low and the induce emf is low the temperature of the ring should not change significantly.

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