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In mixed state of a type-II superconductor, when we allow a transport current to pass through it, we say that the Lorentz force acts and as a result the flux starts flowing, when the force is greater than the pinning force. What i want to know is whether the Lorentz force acts on the electrons present in the normal region or the electrons carrying the transport current. I will be thankful if someone can clear the picture to me.

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This is a subtle--- and occasionally contentious--- issue. It's too complicated to explicate here, but a good basic reference is P. Nozieres and W. F. Vinen "The motion of flux lines in type II superconductors" Philosophical Magazine: A Journal of Theoretical Experimental and Applied Physics, 14:130, 667-688, DOI: 10.1080/14786436608211964.

If you have no access to this journal, you can look at an old paper of mine on the arxiv: arXiv:cond-mat/9708017v1

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