A small magnetic dipole of moment \(\vec{m} = m\hat{z}\) is fixed at the origin. A thin circular ring of radius \(R\) carrying a steady counterclockwise current \(I\) (as viewed from above) lies in a horizontal plane centered at \((0, 0, z)\) on the positive \(z\)-axis, where \(z > 0\). The net vertical magnetic force exerted on the ring by the dipole is given by

\[ F_z = -\dfrac{3\mu_0 m I z R^2}{2(z^2 + R^2)^{5/2}} \]

In the limit where the loop radius is much smaller than the distance to the dipole (\(R \ll z\)), which of the following expressions correctly approximates \(F_z\), and what physical mechanism explains its dependence on \(R\)?