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Currently I'm using Charles Kittel's "Introduction to Solid-State Physics", 8th edition. At chapter 10, Superconductivity, he is deriving an expression for a superconductor with a magnetization M brought close to a magnet. He says that the work done on the superconductor can be given by the integral:

$W=\int_0^{B_a} \vec{M}*\vec{dB_a}$

By considering the superconductor as long with axes parallel with the applied magnetic field he can use the formula:

$\vec{B}=\vec{B_a}+\mu_0 \vec{M}=0$ inside the superconductor.

This means that $\vec{M}=-\frac{\vec{B_a}}{\mu_0}$

Using this identity I could get an expression for dF as:

$dF = \frac{B_a}{\mu_0}dB_a$

One integration would give $F(B_a)-F(0)=\frac{B_a^{2}}{2\mu_0}$

I cannot understand, why isnt $F(0)=0$, it doesnt make sense, no applied magnetic field and yet some sort of force which results in an energy? What have I missed?

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1 Answer 1

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Because F is here free energy which is referred as amount of internal energy of a thermodynamic system that is available to perform work. So system have always free energy which can never be zero even in B=0, OR anything else.. Doesn't matter

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