Question

(10%) Problem 7: 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. His wedding ring has a diameter of 2.35 cm and it takes 0.475 s to move it into the field. Randomized Variables d=2.35 cm t = 0.475 s 33% Part (a) What average current is induced in the ring in A if its resistance is 0.0100 S2? I = 1 Grade Su Deduction Potential E sin cos t ano cotan asin acos atan) acotan sinh) cosho tanho cotanh() Degrees Radians ( ) 7 8 ^^^! 4 5 | = 1 2 + - 0 VO BACKSPACE 9 6 3 . DEL HOME - 4 END CLEAR Submissic Attempts (7% per a detailed Submit Hint Feedback I give up! Hints: 2% deduction per hint. Hints remaining: 2 Feedback: 1% deduction per feedback. 33% Part (b) What average power is dissipated in mw? A 33% Part (c) What magnetic field is induced at the center of the ring in T?

I cannot figure out this one. can someone help?

Answer 1

given
B = 2.00 T
d = 2.35 cm = 0.0235 m
delta_t = 0.475 s

a) induced emf in the ring = A*dB/dt

= (pi*d^2/4)*dB/dt

= (pi*0.0235^2/4)*(2 - 0)/0.475

= 1.826*10^-3 V

induced current in the ring, I = induced emf/R

= 1.826*10^-3/0.01

= 0.183 A <<<<<<<<------------------Answer

b) Power dissipated, P = i^2*R

= 0.183^2*0.01

= 3.35*10^-4 W

= 0.335 mW <<<<<<<<------------------Answer

c) induced magnetic field at the center of the ring, B = mue*I/(2*r)

= 4*pi*10^-7*0.183/(2*0.0235/2)

= 9.78*10^-6 T <<<<<<<<------------------Answer