Question

The electric field in a certain region of space points in the z direction and has magnitude e=5xz where x and z are measured from some origin.calculate the flux of that field through a square perpendicular to the z axis the cprners of the square are at (x,y,z)=(-1,-1,1),(-1,2,1),(2,2,1) and (2,-1,1).

Answer 1

$\phi=\int\int\vec{E}\cdot\vec{dA}\\=\int_{-1}^{2}\int_{-1}^{2}(5xz\hat{k})\cdot(dx dy\hat{k})\\=5z\left(\int_{-1}^{2}dy\right)\left(\int_{-1}^{2}xdx\right)\\=5 \cdot 1 \cdot 3 \cdot \left(\frac{4-1}{2}\right)\\=22.5 \text{units}$