Question

A long thin cylinder rod mode made of paramegnetic with magnetic suspectibilty `chi` and having a cross-carrying coil. One end of the rod is located at the coil centre where the magnetic induction equal to `B` wheares the other end is located in the region where the magnetic field is practically absent. What is the force that the coil exerts on the rod ?

Answer 1

From the formula
`vec(F) = (vec(p_(m)) vec(grad)) vec(B) rarr vec(F) - P int (vec(J). vec(grad)) vec(B) dV`,
Thus, `vec(F) = (chi)/(mu mu_(0)) int (vec(B). vec(grad)) vec(B) dV`
or since `vec(B)` is presominantly along the x-axis,
`F_(x) = (chi)/(mu mu_(0)) int B_(x) (del B_(x))/(del x) Sdx = (chi S)/(2 mu mu_(0)) int_(x = 0)^(x = L) dB_(x)^(2) = (chi SB^(2))/(2 mu mu_(0)) = (chi SB^(2))/(2 mu_(0))`