If a magnet moves near a coil, it generates a changing flux which generates current due to Faraday's Law. Clearly there is no flux when we consider a straight wire, but it seems to me that a current should still form.
Each electron in the wire behaves like a small magnetic dipole (since they rotate around the nucleus). Then since magnets repel/attract each other, shouldn't a permanent magnet placed near a copper wire produce a current by repelling or attracting the electrons? It feels wrong because neither the magnet nor the wire are moving, but I can't see why there shouldn't be a current.