Answer to Question #168440 in Electricity and Magnetism for beth

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 current sheat the stent. Consider a stainless-steel stent 12 mm long by 4.5 mm in diameter, with total resistance 41 mΩ. Treating the stent as a wire loop in the optimum orientation,find the rate of change of magnetic field needed for a heating power of 250 mW.

Answer 1

$\varepsilon=\frac{d\Phi}{dt}=S\frac{dB}{dt},$

$P=\frac{\varepsilon^2}{R},\implies\varepsilon=\sqrt{PR},$

$\frac{dB}{dt}=\frac{\sqrt{PR}}{S}=\frac{4\sqrt{PR}}{\pi d^2},$

$\frac{dB}{dt}=\frac{4\cdot \sqrt{0.25\cdot 0.041}}{3.14\cdot (4.5\cdot 10^{-3})^2}=6.37~\frac{kT}{s}.$