One major example of the Divergence Theorem is Gauss's Law, which is a flux integral:
More information on Divergence Theorem here: Divergence theorem - Wikipedia, the free encyclopedia
One major example of the Divergence Theorem is Gauss's Law, which is a flux integral:
More information on Divergence Theorem here: Divergence theorem - Wikipedia, the free encyclopedia
Stokes I always use to compute flux ? And the divergence theorem ?
example
Determine the flux vector field: through the paraboloid below the plane and vector normal to the surface points to the external side of the paraboloid
I can use Stokes or divergence theorem ?
the flux equal
so how you can use Stokes's theorem for flux is there anti curl because Stoke's
since is the curl of F so if there is an anti for curl you can use Stoke's for flux
but the divergent theorem is
is the gradient
Stoke's theorem change from surface integral to linear integral but divergence theorem change from surface integral to volume
Green's is a special case from Stoke's
that what I think is correct is there any mistake about I said ...
ok show me you should find G such that
you can use Sotke's for flux if they give you a vector like this
so for the flux
you can't use divergence if the surface is not closed if it is closed the integral above equal zero because
because
div for the curl equal zero
ok
curl G = F do you know the curl l determinate l
l....... i...... j...... k............ l
l..... d/dx.. d/dy...... d/dz... l = xi + yj + zk
l ...... f...... h........... g..... l
first you should find the derivative with respect to x,y,z then you should find the f ,h, g after you find them but them like this
I will try to find them
see this link
Paraboloid -- from Wolfram MathWorld