Question

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〉

Answer 1

Flux is zero since asked in $\pi$ is $0\pi$.

Flux is the presence of a pressure field in a detailed physical medium or the glide of electricity through a surface. In electronics, the term applies to any electrostatic field and any magnetic subject. Flux is depicted as "traces" in a plane that contains or intersects electric powered fee poles or magnetic poles.

The definition of flux is a flow of liquid from the body, or a regular movement or exchange. An instance of flux is diarrhea. An example of flux is an ever-converting list of the responsibilities of a particular process. regular or frequent alternate; fluctuation.

Flux is a go-platform computer program that adjusts a show's color temperature in keeping with vicinity and time of day, offering practical respite for the eyes. the program is designed to reduce eye stress at some stage in night-time use, supporting reducing the disruption of sleep patterns.

Our field is IR^3 be,

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

Now divergence theorem says that Flux can be calculated by

$\int\limits^ {} \, F.n = \int\limits^ {} \,( c.F) dv$

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 $\pi$ is $0\pi$.

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