A metallic ring of radius  $r$ and resistance  $R$ is held fixed with its axis along a uniform magnetic field in space whose magnitude is varying with time as  $B_0\sin \left(\omega t\right).$ Neglect gravity. Then

$$\begin{gathered} \varphi =\left(B_0\sin \omega t\right)\pi r^2 \\ \Rightarrow e=-\frac{d\varphi }{dt}=-\pi r^2{B}_0\omega \cos \omega t \\ i=\frac{e}{R}=-\frac{\pi r^2{B}_0\omega }{R}\cos \omega t \\ dF=i\times dl\times B=\left(\frac{\pi r^2{B}_0\omega }{R}\cos \omega t\right)dl\times B_0\sin \left(\omega t\right)\Rightarrow \frac{dF}{dl}\propto B_0^2 \\ H=\int i^{2}Rdt=\int {\left(\frac{\pi r^2{B}_0\omega }{R}\cos \omega t\right)}^{2}Rdt\propto r^4 \end{gathered}$$

Net magnetic force on the ring is zero because force per unit length on diametrically opposite elements is equal in magnitude and opposite in direction.