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I am reading a paper on superconductivity and in it it says that the vortices are subject to a Lorentz force given by $$\vec{F}_L=\frac{\Phi_0\vec{I} \times \vec{H}}{cH}$$ Here $\vec{F}_L$ is the Lorentz force vector, $\Phi_0$ is the flux quantum of a single vortex, $\vec{I}$ is the current, $\times$ is the cross product, $\vec{H}$ is the magnetic field intensity vector and $cH$ (I am guessing) is some fraction of the modulus of $\vec{H}$.

Q1: However, I cannot reconcile this equation with the Lorentz force equation. $F_{L}=q(\vec{E} + \vec{v}\times\vec{B})$, perhaps someone can help me?

Q2: I am also not clear about what exactly the Lorentz force is acting upon. When the magnetic field penetrates the interior of a type II superconductor, the matrix through which it passes is rendered normal and so any electrons there are just normal conducting electrons. Encricling the magnetic field line however are superconducting electrons. It seems to me that as the magnetude of the magnetic field drops off exponentially with distance from the vortex core the population of normal electrons give way to superconducting electrons. - But which is the Lorentz force acting on the normal electrons, superconducting, both?

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