Finding Flux question?

Question

My question is almost the same as the question you see at this link, http://www.licil.org/Tucker/math/physics3.htm (#24-2 Electric Field),

The only differences are the E Field now piercing the Guassian cube is now E=4.0i-3.0(y^2+2.0)j, and find the electric flux through the top face, bottom face, left face, back face, and the net electric flux through the cube.

Just like always SHOW ME AS MUCH WORK AS POSSIBLE, and I have answer I just want to see if it is right, so PLEASE LEAVE AN ANSWER!

Answer 1

For the left and right faces, the element of the area dA has only an x-directed component. The dot product E*dA will be the x-component of E times dA. The x-component of E is the constant 4.0. The flux through the left and right faces is then the area of the face times 4.0. The cube dimensions are 2x2x2, the area of a face is 4, so the flux is 4*4=16.

For the top and bottom face, the dot product involves only the y-component of E which is -3(y^2+2). The area dA is dx*dz, and the y-component of E does not vary with x or z. Again there is the situation where the flux is simply the product of the face area times the field intensity. However, the field intensity for the bottom face (y=0) is -6, and for the top face (y=2) is -18. So flux through bottom is -24, and through top is -72.