A stent is a cylindrical tube, often made of metal mesh, that\'s inserted into a

Question

A stent is a cylindrical tube, often made of metal mesh, that's inserted into a blood vessel to overcome a constriction. It's sometimes necessary to heat the stent after insertion to prevent cell growth that could cause the constriction to recur. One method is to place the patient in a changing magnetic field, so that induced currents heat the stent. Consider a stainless-steel stent 12 mm long by 5.0 mm diameter, with total resistance 39 m Ohm. Treat the stent as a wire loop. a. What is the optimal orientation of the stent with respect to the magnetic field? (Your answer should be a clear sketch and/or brief one-sentence explanation.) b. Find the rate of change of the magnetic field needed for a heating power of 280 mW. In other words, what is dB/dt?

Explanation / Answer

P=280mW =0.28W

R=39 mohms =0.039 ohms

P=I^2R

I=sqrt(P/R ) =sqrt(0.28/0.03)

I=3.05A

r=D/2 =5/2 =2.5mm

Area A=pir^2 =pi*(2.5*10^-3)^2 =1.96*10^-5 m^2

E=A(dB/dt)

IR =A(dB/dt)

dB/dt =IR/A =(3.05*0.039/1.96*10^-5)

dB/dt = 6.06KT/s

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