How do I specify a boundary condition with curl?

I’m solving TDGL on a 2D circular domain.
I don’t know how to specify the boundary condition for the vector potential A.
One of the BC is that curl A = B, where B is the given magnetic field.
In the variational form, this becomes a line integral along the boundary.
But the line integral contains dot product, how should I deal with this?

Thank you.

it might help you to look at the following couple of lines (part of “problem” definition) :
// boundary condition on superconductor: B is perpendicular to the surface, Bn=0
+ int1d(Th,1,2)((-dy(Aphi)*N.x+dx(Aphi)*N.y)*v)
that I have used for a curved superconducting boundary in a cylindrical geometry.
The applied magnetic field was along Oz, the axis of revolution of the system. So vector potential is orthoradial, i.e. only Aphi is non zero.