HW Help. Part A,B,C and D please! Show work. Problem 25.61 - MC 8 of 8 Constants

Question

HW Help. Part A,B,C and D please! Show work.

Problem 25.61 - MC 8 of 8 Constants Part A 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 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 1.9 T to 0 Tin 0.4 s, as it might in an MRI solenoid (Figure 1) What is the induced emf in the loop? Express your answer using three significant figures using the proper unit. View Available Hint(s) arm or leg. Muscle End ValueUnits Submit Part B What is the power dissipated by the loop while the magnetic field is changing? Hint Given the resistivity of muscle tissue, the loop would have a resistance of 41.6 Express your answer using three significant figures and include the appropriate unit. View Available Hint(s) Figure 1 of 1 > 8.0 cm PValue Units Submit 1.0 cm Part C How much heat is created by the loop while the magnetic field is changing? (Assume that all of the power dissinated is changed into heat

Explanation / Answer

magnetic flux = B*A

induced emf = -rate of change in magnetic flux

emf e = -A*dB/dt = -A*(B2-B1)/t

A = are of cross section = pi*r^2

r = radius = 8/2 cm =4 cm = 4*10^-2 m

B2 = 0

B1 = 1.9 T

time t = 0.4 s

emf , e = -pi*(4*10^-2)^2*(0-1.9)/0.4 = 2.39*10^-2 V

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part B

power dissipated P = e^2/R

R = resistance

P = (2.39*10^-2)^2/(41.6*10^3)

P = 1.37*10^-8 W

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part ( c )

heat created Q = P*t = 1.37*10^-8*0.4 = 5.48*10^-9 J

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part(D)

heat gained Q = m*S*dT

5.48*10^-9 = 22*10^-3*3600*dT

change in temperature dT = 6.9*10^-11 oC

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