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Chapter 1: Q2P (page 4)
Is the cross product associative?
If so, prove it; if not, provide a counterexample (the simpler the better).
The values of the two cross product and , are not equal. Thus.
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Express the cylindrical unit vectors in terms of (that is, derive Eq. 1.75). "Invert" your formulas to get in terms of
Test Stokes' theorem for the function , using the triangular shaded area of Fig. 1.34.
Check Stokes' theorem using the function (aand bare constants) and the circular path of radius R,centered at the origin in the xyplane. [Answer: ],
A uniform current density fills a slab straddling the plane, from to . A magnetic dipole 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 direction: .
(c) In the electrostatic case, the expressions and are equivalent (prove it), but this is not the case for the magnetic analogs (explain why). As an example, calculate for the configurations in (a) and (b).
Calculate the curls of the vector functions in Prob. 1.15.
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