Answer to Question #329860 in Electricity and Magnetism for Nati

Question

A very large, superconducting solenoid such as one used in MRI scans, stores 1.00 MJ of energy in its magnetic field when 100 A flows. (a) Find its self-inductance. (b) If the coils

“go normal,” they gain resistance and start to dissipate thermal energy. What temperature increase is produced if all the stored energy goes into heating the 1000 kg magnet,

given its average specific heat is 200 J/kg·oC ?

Answer 1

a)

$W=\frac{LI^2}2,$

$L=\frac{2W}{I^2}=20~kH.$

b)

$W=cm∆t,$

$∆t=\frac W{cm}=5°C.$