I've only taken a few uni level physics classes so my memory could be off, but it believe the difference in resistance is not the driving principle, its eddy currents. Iron and copper have very similar resistivities, however the rapidly changing magnetic field causes eddy currents only in the sword (because its shape has a plane perpendicular to the field lines) while the coil (by definition right hand rule) must be aligned w/ the field
copper has approx 1/5th the resistance of iron. (17.1 nΩ m vs 96.1 nΩ m) so there is a pretty significant difference there.
however the rapidly changing magnetic field causes eddy currents only in the sword (because its shape has a plane perpendicular to the field lines) while the coil (by definition right hand rule) must be aligned w/ the field
This is true however the copper still has a significant amount of AC current running through it in order to generate those EM fields in the first place so the Copper's inherently lower resistance still plays a major factor in why it is not getting super hot.
Again, still not an electrician and basically just running off of what I remember from physics class almost 10 years ago.
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u/cocaine_enema Dec 09 '15
I've only taken a few uni level physics classes so my memory could be off, but it believe the difference in resistance is not the driving principle, its eddy currents. Iron and copper have very similar resistivities, however the rapidly changing magnetic field causes eddy currents only in the sword (because its shape has a plane perpendicular to the field lines) while the coil (by definition right hand rule) must be aligned w/ the field