In Prob. 6.4, you calculated the force on a dipole by “brute force.” Here’s a more elega...

In Prob. 6.4, you calculated the force on a dipole by “brute force.” Here’s a more elegant approach. First write B(r) as a Taylor expansion about the center of the loop:

where r0 is the position of the dipole and ∇₀ denotes differentiation with respect to r₀. Put this into the Lorentz force law (Eq. 5.16) to obtain

Or, numbering the Cartesian coordinates from 1 to 3:

where δi _j is the Kronecker delta (Prob. 3.52).