The electric field components as shown in the figure are , , in which . We have to calculate (a) the flux through the cube and (b) the charge within the cube. We may assume that .

Solution:             Click For PDF Version

(a)

The electric field components as shown in the figure are , , in which . Therefore, the non-zero contributions to the flux due to the electric field to the Gaussian surface of the cube places with respect to the coordinate axes will be from the Y-Z faces located at and , where .

Therefore,

(b)

The charge q inside the cube can be calculated using the Gauss’ law