In a perfect conductor, the conductivity is infinite, so E = 0 (Eq. 7.3), and any net charge resides...

Question

In a perfect conductor, the conductivity is infinite, so E = 0 (Eq. 7.3), and any net charge resides on the surface (just as it does for an imperfect conductor, in electrostatics).

(a) Show that the magnetic field is constant ( = 0), inside a perfect conductor.

(b) Show that the magnetic flux through a perfectly conducting loop is constant. A superconductor is a perfect conductor with the additional property that the (constant) B inside is in fact zero. (This "flux exclusion" is known as the Meissner effect.³⁰)

(c) Show that the current in a superconductor is confined to the surface.

(d) Superconductivity is lost above a certain critical temperature (T_c), which varies from one material to another. Suppose you had a sphere (radius a) above its critical temperature, and you held it in a uniform magnetic field B₀ while cooling it below T_c. Find the induced surface current density K, as a function of the polar angle θ.

Robert · Accepted Answer

Solution:- 
(a) In a perfect conductor E=0 
Then from Faradays lay says 0
( )
B
E
t
B
thus
t
Thus B r isrepresents of t

  





(b.)From integral form of faraday’slaw 
.

In a perfect conductor, the conductivity is infinite, so E = 0 (Eq. 7.3), and any net charge resides on the surface (just as it does for an imperfect conductor, in electrostatics). (a) Show that the...

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