# Is the surface integral of a vector field through the six surfaces of a cube zero?

Is the surface integral of a vector field through the six surfaces of a cube zero when the vector field is defined in the whole region. If I integrate over all the surfaces for any vector field. The flux through opposite surfaces cancel out. So is this true for a cube?

• What makes you thing that opposite faces will always cancel? – amd Aug 4 '18 at 2:07
• @amd for a vector field when we are integrating over a region and vector field is A then A.n Is always equal for both faces in value but sign is always opposite in opposite faces . So surface integral of both added is zero. I think. Where's my mistake. I just wanna know my mistake. – user187604 Aug 4 '18 at 7:59
• Try it with the field $\mathbf r/\|\mathbf r\|$, where $\mathbf r = (x,y,z)$. – amd Aug 6 '18 at 0:25