A uniform current density J = J 0 z fills a slab straddling the yz plane, from

Question:

A uniform current density J = J₀ z fills a slab straddling the yz plane, from x = – a to x = + a. A magnetic dipole m = m₀ x is situated at the origin.

(a) Find the force on the dipole, using Eq. 6.3.

(b) Do the same for a dipole pointing in the y direction: m = m₀y.

(c) In the electrostatic case the expressions F = ∆(p ∙ E) and F = (p ∙ ∆)E are equivalent (prove it), but this is not the case for the magnetic analogs (explain why). As an example, calculate (m ∙ ∆) B for the configurations in (a) and (b).