0 (recall E = J/o) and net charge 2. Conductivity o in a perfect conductor is...

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0 (recall E = J/o) and net charge 2. Conductivity o in a perfect conductor is infinite, so E resides on the surface (just like an imperfect conductor in electrostatics). (a) Show that the magnetic field is time-independent inside a perfect conductor. (b) Show that the magnetic flux through a perfectly conducting loop is time-independent. A superconductor is a perfect conductor with the additional property that the time-independent field B is in fact zero inside the conductor. (c) Show that the current in a superconductor is confined to the surface. (d) Superconductivity is lost above a certain critical temperature (T.), which varies from one ma- terial to another. Suppose you had a sphere with radius a above its critical temperature, and you held it in a uniform magnetic field Bo2 while cooling it below T.. Find the induced surface current density K, as a function of the polar angle 0. 0 (recall E = J/o) and net charge 2. Conductivity o in a perfect conductor is infinite, so E resides on the surface (just like an imperfect conductor in electrostatics). (a) Show that the magnetic field is time-independent inside a perfect conductor. (b) Show that the magnetic flux through a perfectly conducting loop is time-independent. A superconductor is a perfect conductor with the additional property that the time-independent field B is in fact zero inside the conductor. (c) Show that the current in a superconductor is confined to the surface. (d) Superconductivity is lost above a certain critical temperature (T.), which varies from one ma- terial to another. Suppose you had a sphere with radius a above its critical temperature, and you held it in a uniform magnetic field Bo2 while cooling it below T.. Find the induced surface current density K, as a function of the polar angle 0.