Question

Use the Divergence Theorem to compute the net outward flux of the following field across the given surface S.

F = (5y - 2x, z - y, 5y - 3x)
S consists of the faces of the cube < 2, .
The outward flux is____. (Type an exact answer)

Answer 1

To compute the net outward flux of the given vector field F across the surface S, use the Divergence Theorem and evaluate the triple integral over the volume enclosed by the surface.

Step-by-step explanation:

To compute the net outward flux of the given vector field F across the surface S, we can use the Divergence Theorem. The Divergence Theorem states that the net outward flux of a vector field across a closed surface is equal to the triple integral of the divergence of the field over the volume enclosed by the surface.

In this case, the surface S consists of the faces of a cube with the equation |x| < 2, |y| < 2, |z| < 2. To find the net outward flux, we need to compute the divergence of the given field F and evaluate the triple integral over the volume enclosed by the cube.

After evaluating the triple integral, the net outward flux of the field F across the surface S is the result of the calculation.

This represents the total flow of the vector field across the cube's surface, illustrating the application of the Divergence Theorem in calculating flux through a closed surface.