Question

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 mm³ is attributed to a pole of the electromagnet M. The magnetic induction at the axis of the poleshoe depends on the height x as B = B₀ exp (—ax²), where B₀ = 1.50 T, a = 100 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 μN.

Answer 1

The force in question is,

since B is essentially in the x-direction,

This is maximum when its derivative vanishes