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Find the net outward flux of f=a×r across any smooth closed surface in r3, where a is a constant nonzero vector and r=〈x,y,z〉

Sagot :

Flux is zero since asked in [tex]\pi[/tex] is [tex]0\pi[/tex].

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Our field is IR^3 be,

F= (bz-cy,cx-az,ay-bx)

Now divergence theorem says that Flux can be calculated by

[tex]\int\limits^ {} \, F.n = \int\limits^ {} \,( c.F) dv[/tex]

Now let's calculate the divergence of a vector field

F = (ia/ax + ja/ay + k*a/az)*((bz-cy)i+((x-dz))+(ay-bx)*k)

a/ax(bz-cy)+a/ay(cx-az)+a/az(ay-bx)

= 0+0+0

=0

Flux is zero since asked in [tex]\pi[/tex] is [tex]0\pi[/tex].

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