Let's look at a super conductor: so resistivity really is zero exactly, and some of our...

Let's look at a super conductor: so resistivity really is zero exactly, and some of our electrostatics assumptions about E=0 in a conductor and the charge is all on the surface really are true

a) Show the magnetic field must be constant inside

b) If you built a loop out of superconducting material, show that the magnetic flux through that loop must be constant

c) Turns out B is not only constant in a super conductor, but zero. Why? Eddy currents on the surface create B equal and opposite to whatever you're throwing at it to cancel out B and make it zero inside. Show why the currents must be all on the surface of the superconductor.

d) Superconductivity is caused by electrons forming so-called "Cooper Pairs" that slalom around the atoms and never slowing down, or transferring energy to heat, or causing resistance.There is a critical temperature where electron pairs rattle apart and atoms vibrate so much that you can't dodge them anyway. What if you made a ball of this stuff above the critical temperature and stuck a magnetic field B₀ in the z-direction through it. Then dump the liquid nitrogen so it cools enough to superconduct. Find the induced surface current K as a function of angle (theta) from the z-axis.

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genius_generous answered 1 year ago

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