A thin, rigid wire bent into a semicircle of radius \(R\) lies in the \(xy\)-plane with its center of curvature at the origin, occupying the region \(y \ge 0\). The wire carries a steady current \(I\) directed counterclockwise from \((R, 0, 0)\) to \((-R, 0, 0)\). A uniform magnetic field \(\vec{B}\) of magnitude \(B_0\) lies in the \(yz\)-plane and makes a constant angle \(\phi\) with the positive \(y\)-axis, such that \(\vec{B} = B_0\cos\phi\,\hat{j} + B_0\sin\phi\,\hat{k}\), where \(0 < \phi < \dfrac{\pi}{2}\). Which of the following expressions represents a correct integral setup to determine the \(z\)-component of the net magnetic force, \(F_z\), exerted on the wire?