All Problems

Constant Magnetic Field, Magnetics

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 mm3V=41 \mathrm{~mm}^{3} is attrabted to a pole of the electromagnet M.M . The magnetic induction at the axis of the poleshoe depends on the height xx as B=B0B=B_{0} exp (ax2),\left(-a x^{2}\right), where B0=1.50 T,a=100 m2.B_{0}=1.50 \mathrm{~T}, a=100 \mathrm{~m}^{-2} . Find: (a) at what height xmx_{m} the ball experiences the maximum attraction; (b) the magnetic susceptibility of the paramagnetic if the maximum attraction force equals Fmax=160μNF_{\max }=160^{\circ} \mu \mathrm{N}.

Reveal Answer
(a) xm=1/4ax_{m}=1 / \sqrt{4 a} (b) χ=μ0Fmaxe/a/VB02=3.6104\chi=\mu_{0} F_{\max } \sqrt{\mathrm{e} / \mathrm{a}} / \mathrm{V} B_{0}^{2}=3.6 \cdot 10^{-4}