Let f = (ax + by + 4z) i + (x + cz) j + (9y + mx) k where a, b,c, and m are constants.a.suppose that the flux of f through any closed surface is 0. which of the constants can be determined?
Accepted Solution
A:
Let [tex]\mathcal R[/tex] be an arbitrary closed region with boundary the surface [tex]\mathcal S[/tex]. By the divergence theorem,
We're assuming [tex]\mathcal R[/tex] is a closed region, and the integral above is its volume, which must be positive. This means we must have [tex]a=0[/tex].