The Meissner effect expels magnetic field lines in a super conductor, see the picture below. Left is normal conducting, right is the superconducting state.
If I have a superconducting wire of radius $r_0$ now, the Meissner effect leads to $B(r<r_0)=0$. When I drive a current $J(r<r_0)=J_0$ this current leads to zero forces when calculating the force using the Lorentz force: $f=j\times B = 0$.
This would mean that all superconducting coils experience no forces. What am I missing here?