What does it mean if the flux integral is zero?

If the vector field F represents the flow of a fluid, then the surface integral of F will represent the amount of fluid flowing through the surface (per unit time). On the other hand, if water is flowing parallel to the surface, water will not flow through the surface, and the flux will be zero.

Can flux of a vector field be zero?

If there are is no enclosed charge by a given surface, then the flux is zero.

What does it mean if the curl of a vector field is zero?

Curl indicates “rotational” or “irrotational” character. Zero curl means there is no rotational aspect to vector field. Non-zero means there is a rotational aspect.

How do you determine whether a vector field is conservative or not?

As mentioned in the context of the gradient theorem, a vector field F is conservative if and only if it has a potential function f with F=∇f. Therefore, if you are given a potential function f or if you can find one, and that potential function is defined everywhere, then there is nothing more to do.

Can you have a negative flux?

Yes, electric flux can be a negative number. When electric lines emerge out of surface, the electric flux is positive and when those lines enter into a surface, the electric flux in negative.

What does negative flux mean?

Remember our convention for flux orientation: positive means flux is leaving, negative means flux is entering. In this example, water is falling downward, or entering the tube. This means the top surface has negative flux (it appears to be siphoning up water).

How much is the electric flux through a closed surface?

The total of the electric flux out of a closed surface is equal to the charge enclosed divided by the permittivity. The electric flux through an area is defined as the electric field multiplied by the area of the surface projected in a plane perpendicular to the field.

How do you know if flux is negative or positive or zero?

When the field vectors are going the opposite direction as the vectors normal to the surface, the flux is negative. When the field vectors are orthogonal to the vectors normal to the surface, the flux is zero.

What if the curl is 0?

If the curl is zero, then the leaf doesn’t rotate as it moves through the fluid. Note that the curl of a vector field is a vector field, in contrast to divergence. Thus, this matrix is a way to help remember the formula for curl.

Can curl of a vector be zero?

the field, the curl is zero. called a conservative ficld. (Such fields have the property that the line integral around any closed loop, often representing the work done in moving a particle, is zero.) A rotational vector is a vector field whose curl can never be zero.

Why does a conservative field have zero curl?

Because by definition the line integral of a conservative vector field is path independent so there is a function f whose exterior derivative is the gradient df. Than the curl is *d(df)=0 because the boundary of the boundary is zero, dd=0.

How do you know if a vector field is solenoidal?

If there is no gain or loss of fluid anywhere then div F = 0. Such a vector field is said to be solenoidal.

What is the vector flux through a closed surface?

I learned that the vector flux through any closed surface is always 0. So if you have a sphere(closed surface) and you put it in an uniform electric field, then the total flux is 0. However, the Gauss’s law states that the electric field flux through a closed surface equals the enclosed charge divided by the permitivity of free space.

Does divergence of 0 everywhere imply that flux is zero?

Answer Wiki. no. So divergence of 0 everywhere implies that the flux for any closed surface is 0 – but it doesn’t mention non-closed surfaces. Of course it is possible that some non-closed surface has a flux of 0, but that doesn’t always happen.

Is the divergence of a non-closed surface always 0?

So divergence of 0 everywhere implies that the flux for any closed surface is 0 – but it doesn’t mention non-closed surfaces. Of course it is possible that some non-closed surface has a flux of 0, but that doesn’t always happen. For example, the vector field F → ( x, y, z) = 5 i ^ has a divergence of ∇ ⋅ F → = 0.

How do you find the flux of a vector field?

Find the flux of the vector field in the negative z direction through the part of the surface z=g(x,y)=16-x^2-y^2 that lies above the xy plane (see the figure below). For this problem: It follows that the normal vector is <-2x,-2y,-1>. Computing Fo<-2x,-2y,-1>, we have Here we use the fact that z=16-x^2-y^2. Hence, the integral becomes