A Uniform Current Density J J0 Z Fills A

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).

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