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 \(F_{\max }=160^{\circ} \mu \mathrm{N}\).