Solved: At temperatures near absolute zero, Bc approaches

Chapter 29, Problem 29.45

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At temperatures near absolute zero, \(B_{\mathrm{c}}\) approaches 0.142 T for vanadium, a type-I superconductor. The normal phase of vanadium has a magnetic susceptibility close to zero. Consider a long, thin vanadium cylinder with its axis parallel to an external magnetic field \(\overrightarrow{\boldsymbol{B}}_0\) in the +x-direction. At points far from the ends of the cylinder, by symmetry, all the magnetic vectors are parallel to the x-axis. At temperatures near absolute zero, what are the resultant magnetic field \(\overrightarrow{\boldsymbol{B}}\) and the magnetization \(\overrightarrow{\boldsymbol{M}}\) inside and outside the cylinder (far from the ends) for (a) \(\overrightarrow{\boldsymbol{B}}_0=(0.130 \mathrm{~T}) \hat{i}\) and (b) \(\overrightarrow{\boldsymbol{B}}_0=(0.260 \mathrm{~T}) \hat{\boldsymbol{i}}\) ?