Problem 3.286

In the arrangement shown in Fig. 3.77 it is possible to measure (by means of a balance) the force with which a paramagnetic ball of volume $V=41 \mathrm{~mm}^{3}$ is attrabted to a pole of the electromagnet $M .$ The magnetic induction at the axis of the poleshoe depends on the height $x$ as $B=B_{0}$ exp $\left(-a x^{2}\right),$ where $B_{0}=1.50 \mathrm{~T}, a=100 \mathrm{~m}^{-2} .$ Find: (a) at what height $x_{m}$ the ball experiences the maximum attraction; (b) the magnetic susceptibility of the paramagnetic if the maximum attraction force equals $F_{\max }=160^{\circ} \mu \mathrm{N}$.