A straight wire of length \(L\) lies along the \(x\)-axis from \(x = 0\) to \(x = L\) and carries a constant current \(I\) in the \(+x\)-direction. The wire sits in a non-uniform magnetic field directed in the \(+z\)-direction whose magnitude increases linearly with position according to \(B(x) = B_0 + Cx\), where \(B_0\) and \(C\) are positive constants. The total magnetic force on the wire is given by \(F = I L B_{\text{avg}}\), where \(B_{\text{avg}} = B(L/2)\) is the field magnitude at the midpoint of the wire. Which of the following provides the correct physical and mathematical explanation for why the net force depends on \(B(L/2)\)?