myfunkymaths said:Homework Statement
calculate net outward flux of vector field F(x,y,z)=3xy^2 i +xcosz j +z^3k, across surface solid bounded by cylinder y^2 +z^2 =1
planes x=-1, x=2
Homework Equations
The Attempt at a Solution
my attempt was triple integral of divF=> 3*triple integral r^3
ended up getting an answer =3pi + (3pi/2)
is the answer i got correct?
thank you
You forgot to multiply by r when converting to polarDick said:No, I don't think so. 3r^2 is ok for an integrand. How did you do the rest?
ƒ(x) said:You forgot to multiply by r when converting to polar
The net outward flux of a vector field across a surface solid is a measure of the total flow of the vector field passing through the surface in an outward direction. It takes into account both the magnitude and direction of the vector field at each point on the surface.
The net outward flux is calculated using a mathematical formula called the surface integral, which involves integrating the vector field over the surface. This calculation takes into account the orientation of the surface and the magnitude and direction of the vector field at each point on the surface.
The net outward flux of a vector field is affected by the magnitude and direction of the vector field, as well as the orientation and size of the surface. It also depends on the distance between the surface and the source of the vector field.
The net outward flux of a vector field has many real-world applications, including in fluid dynamics, electromagnetism, and thermodynamics. It is used to calculate the rate of flow of fluids, the strength of electric and magnetic fields, and the transfer of heat and energy in various systems.
The net outward flux of a vector field is mathematically related to the divergence of the vector field. The divergence of a vector field at a point represents the tendency of the vector field to flow outward from that point. The net outward flux is a measure of this tendency over a larger surface or region.