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A uniform magnetic field ?B has constant strength ?b teslas in the ?z-direction [i.e., ?=〈0,0,?〉B=〈0,0,b〉 ]...

A uniform magnetic field ?B has constant strength ?b teslas in the ?z-direction [i.e., ?=〈0,0,?〉B=〈0,0,b〉 ]

(a) Verify that ?=12?×?A=12B×r is a vector potential for ?B, where ?=〈?,?,0〉r=〈x,y,0〉
(b) Calculate the flux of ?B through the rectangle with vertices ?A, ?B, ?C, and ?D in Figure 17.

?=(6,0,2),?=(6,4,0),?=(0,4,0),

?=(0,0,2),?=(6,0,0)

Flux(?)=

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