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In a course on superconducting materials, my lecturer has suggested that in a Type I(one) superconductor, any normalconducting region containing trapped magnetic flux will feel a Lorentz force per unit volume [tex]F_L = J \times B[/tex], where [tex]J[/tex] is the transport current density (

**vector!**) that the material is carrying, and [tex]B[/tex] is a vaguely-defined magnetic flux density.

He goes on to define the "critical current density" [tex]J_c[/tex] by the equality [tex]J_c \times B = -F_p[/tex] where [tex]F_p[/tex] is a force per unit volume due to pinning of the flux lines on some kind of material defect.

My problems with this are:

- Concept - how can a non-charged body feel a Lorentz force? (This is probably solved by thinking about a supercurrent that surrounds the flux-containing region...)
- What is [tex]B[/tex], given that the Meissner effect excludes magnetic fields in superconducting regions? Could is be the externally-applied field, measured at a distance? Or the (higher) flux density
**inside**the flux-containin region of the material? - How can I reconcile my lecturer's definition of [tex]J_c[/tex] with the more generally-available definition: "the maximum current a superconductor can carry before making a transition back to normal conduction"?

Any help would be much appreciated, as I'm very stuck on this concept and I can't find any online resources which mention this particular phenomenon - thanks!