A rigid, straight wire segment of length \(L\) and mass \(m_0\) lies along the \(x\)-axis on a digital balance in a horizontal plane. A constant current \(I\) flows through the wire in the \(+x\)-direction. A standard right-handed Cartesian coordinate system is defined where the \(+z\)-axis points vertically upward and the \(+y\)-axis is horizontal and perpendicular to the wire. When a uniform magnetic field \(\vec{B}\) is applied to the region containing the wire, the balance reading increases by an amount \(\Delta m\). Which of the following correctly pairs the minimum magnitude \(B_{\text{min}}\) of the magnetic field with the direction in which \(\vec{B}_{\text{min}}\) must point?