Let's look at a super conductor: so resistivity really is zeroexactly, and some of our electrostatics assumptions about E=0 in aconductor 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, showthat the magnetic flux through that loop must be constant
c) Turns out B is not only constant in a super conductor, butzero. Why? Eddy currents on the surface create B equal and oppositeto whatever you're throwing at it to cancel out B and make it zeroinside. Show why the currents must be all on the surface of thesuperconductor.
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 acritical temperature where electron pairs rattle apart and atomsvibrate so much that you can't dodge them anyway. What if you madea ball of this stuff above the critical temperature and stuck amagnetic field B0 in the z-direction through it. Thendump the liquid nitrogen so it cools enough to superconduct. Findthe induced surface current K as a function of angle (theta) fromthe z-axis.
