Explanation :
Energy in magnetic system
$ \;W_f=\int\limits_0^\lambda i(\lambda)d\lambda $
$ \because\;\mathrm i=\mathrm\lambda^2\cdot\mathrm g^2 $ Given
$ \;W_f=\int\limits_0^\lambda\lambda^2.g^2.d\lambda=g^2.\frac{\lambda^3}2 $
Now, mechanical force,
$ \begin{array}{l}\;{\mathrm F}_\mathrm F=-\frac{\partial{\mathrm W}_\mathrm f(\mathrm\lambda,\mathrm g)}{\partial\mathrm g}\\\;\;\;\;\;=\frac\partial{\partial\mathrm g}\left(\frac{\mathrm g^2\cdot\mathrm\lambda^3}3\right)=\frac23\mathrm\lambda^3\cdot\mathrm g\\\because\mathrm i=2\mathrm A,\mathrm g=10\mathrm{cm},\mathrm\lambda=10\sqrt2\end{array} $
Hence,$\left|{\mathrm{F}}_{\mathrm{F}}\right|=\frac{2}{3}\times {\left(10\sqrt{2}\right)}^{3}\times 0.1$
$=188.56\mathrm{N}$