Currents induced by rapid field changes in an MR I solenoid can. in some cases,

Question

Currents induced by rapid field changes in an MR I 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 1.7 T to 0 T in 0.1 s. as it might in an MRI solenoid. What is the induced emf in the loop? Express your answer using three significant figures using the proper unit. epsilon) ind = What is the power dissipated by the loop while the magnetic field is changing? Express your answer using three significant figures and include the appropriate unit. P = How much heat is created by the loop while the magnetic field is changing? (Assume that all of the power dissipated is changed into heat.) Express your answer using three significant figures and Include the appropriate unit. H = By how much will the temperature of the tissue increase? Assume that muscle tissue has specific heat 3600 J/(kg middot C^lambda) delta T =

Explanation / Answer

a)

Induced emf, E = change in flux / time = (1.7 - 0)/0.1 = 17 V

b)

Power dissipated, P = E^2/R

= 17^2/(41.6*10^3)

= 6.9*10^-3 W

c)

Heat created, H = P*t

= 6.9*10^-3*0.1

= 6.9*10^-4 J

d)

H = m*C*T

So, 6.9*10^-4 = 0.022*3600*T

So, T = 8.7*10^-6 deg C <------answer

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