| Face | \(\mathbf{n}\) | \(\mathbf{F}\) | \({\bf F} \,{\cdot}\, {\bf n}\) | \(\rho \iint\limits_{\kern-8ptS}\mathbf{F}\,{\cdot}\, \mathbf{n}\,dS\) | |
|---|---|---|---|---|---|
| \(S_{1}={\it ABCO}\) | \(z=0\) | \(-\mathbf{k}\) | \(-y^{2}\mathbf{j}\) | 0 | 0 |
| \(S_{2}={\it OAEG}\) | \(y=0\) | \(-\mathbf{j}\) | \(4xz\mathbf{i}\) | 0 | 0 |
| \(S_{3}={\it OCDG}\) | \(x=0\) | \(-\mathbf{i}\) | \(-y^{2}\mathbf{j}+yz\mathbf{k}\) | 0 | 0 |
| \(S_{4}={\it ABFE}\) | \(x=1\) | \(\mathbf{i}\) | \(4z\mathbf{i}-y^{2}\mathbf{j}+yz\mathbf{k}\) | \(4z\) | \(\rho \int_{0}^{1}\int_{0}^{1}4z\,dy\,dz=2\rho\) |
| \(S_{5}={\it BCDF}\) | \(y=1\) | \(\mathbf{j}\) | \(4xz\mathbf{i}-\mathbf{j}+z\mathbf{k}\) | \(-1\) | \(-\rho \int_{0}^{1}\int_{0}^{1}\,dx\,dz=-\rho\) |
| \(S_{6}={\it DFEG}\) | \(z=1\) | \(\mathbf{k}\) | \(4x\mathbf{i}-y^{2}\mathbf{j}+y\mathbf{k}\) | \(y\) | \(\rho\int_{0}^{1}\int_{0}^{1}y\,dx\,dy=\dfrac{1}{2}\rho\) |