Problem 25.61-MC 8of8> Currents induced by rapid field changes in an MRI solenoi

Question

Problem 25.61-MC 8of8> Currents induced by rapid field changes in an MRI solenoid can, in some cases, heat tissues in the body but under normal circumstances the heating is small. We can do a quick estimate to show this. Consider the loop" of muscle tissue shown in the figure. This might be muscle circling the bone of your arm or leg. Muscle tissue is not a great conductor, but current will pass through muscle and so we can consider this a conducting loop with a rather high resistance. Suppose the magnetic field along the axis of the loop drops from 1.6 T to 0 T in 0.2s, as it might in an MRI solenoid. (Figure 1) Part A What is the induced emf in the loop? Express your answer using three significant figures using the proper unit. View Available Hint(s) 64-10V Submit X Incorrect; Try Again igure

Explanation / Answer

for the given data

dB = 1.6 - 0 = 1.6 T

D = 8 cm ( diameter of muscle loop)

t = 1 cm ( thichness of muscle fibre)

a. induced EMF = -d(phi)/dt

phi = pi*D^2*B/4

V = -d(phi)/dt = pi*D^2*1.6/4 = 0.4*pi*D^2

V = 0.008042477193189870 V

b. Resistacen, R = 41.6 kohms

hence

power dissipated P = V^2/R = 1.55484*10^-9 W

c. heat = power dissipated * time = 1.55484*10^-9*0.2 = 3.109*10^-10 J

d. specific heat, c = 36,000 J/kg C

hence 1/dT = 36,000*0.022 / 3.109*10^-10

dT = 3.92*10^-13 C

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