Question

Let S be the cube with side length 2, faces parallel to the coordinate planes, and centered at the origin. (a) Calculate the total flux of the constant vector field out of S by computing the flux through each face separately. (b) Calculate the flux out of S for any constant vector field.

a) Bold response required
b) Flux can't be calculated for a cube
c) Vector fields are not applicable
d) Vector calculus is not suitable

Answer 1

The total flux of a constant vector field out of the cube can be calculated by computing the flux through each face separately. The net flux through the cube is zero.

Step-by-step explanation:

The total flux of a constant vector field out of the cube can be calculated by computing the flux through each face separately. Let's consider the cube with side length 2 centered at the origin with faces parallel to the coordinate planes.

To find the flux through each face, we need to consider the orientation of the face relative to the direction of the electric field. For the bottom face of the cube, the flux is negative because the area vector points downward. Along the other four sides, the direction of the area vector is perpendicular to the direction of the electric field, resulting in zero flux. So, the net flux through the cube is zero.