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 1.70 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 0.340 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.)

b.) What average power is dissipated (in W)?

c.) What average magnetic field is induced at the center of the ring? (Enter the magnitude in teslas.)

d.) What is the direction of this induced magnetic field relative to the MRI's field?

Explanation / Answer

Given,

B = 1.7T ; d = 2.19 cm ; T = 0.34 s

A = 3.14 x (0.0219/2)^2 = 0.00038 m^2

a)We know that the induced emf is given by:

e = -d(phi)/dt

e = -A b(B)/dt

e = 0.00038 x 1.7/0.34 = 1.9 x 10^-3 V

I = V/R = e/R

I = 1.9 x 10^-3/0.01 = 0.19 A

Hence, I = 0.19 A

b)P = I^2 R

P = 0.19^2 x 0.01 = 3.61 x 10^-4 W

Hence, P = 3.61 x 10^-4 W

c)B = u0 I/2 pi r

B = 4 pi x 10^-7 x 0.19/ 2 pi x 0.01095 = 3.47 x 10^-6 T

Hence, B = 3.47 x 10^-6 T

d)Parallel to the MRI feild.

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