Question

Question Part Points Submissions Used An MRI technician moves his hand from a region of very low magnetic field strength into an MRI scanner's 2.50 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 0.330 s to move it into the field. (a) What average current is induced in the ring if its resistance is 0.0100 Ω? (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.

Answer 1

Given,

B1 = 0 ; B2 = 2.5 T ; d = 2.19 cm ; t = 0.33 s

r = 2.19/2 = 1.095 cm

a)R = 0.01 Ohm

because of the change in B field there will be a change of magentic flux and an emf will be induced

emf = -d(phi)/dt

emf = A (B2 - B1)/t

emf = 3.14 x 0.01095^2 (2.5 - 0)/0.33 = 0.0029 V

from Ohm's law, V = IR

I = V/R = emf/R

I = 0.0029/0.01 = 0.29 A

Hence, I = 0.29 A

b)P = I^2 R

P = 0.29^2 x 0.01 = 0.0008 W

Hence, P = 0.0008 W

c)B = u0 I/2 R

B = 4 pi x 10^-7 x 0.29/(2 x 0.01095) = 1.66 x 10^-5 T

Hence, B = 1.66 x 10^-5 T

d)Out of the page