Assume that the Dirac string is lying along the negative $z$-axis, and is subject to a magnetic field $B$. Assume throughout this question that we are considering a static situation. The force on the Dirac string is given by
$$F=g\int_{-\infty}^0 dz'\nabla '(e_z\cdot B)$$
Assuming a) $B$ vanishes at infinity i need to show $$F_z=gB_z(x=0,y=0,z=0)$$ and also b) $$\nabla \times B = 0 $$ and c) in general
$$F=gB(x=0,y=0,z=0)$$
But isnt the first question obvious if $e_z \cdot B = B_z$ and the integral and del operator cancels. And this will indicate the third question being valid too?