Alright, guys, let's work this one out together. So we have a cube and its side length is two centimeters and it's placed in a uniform electric field. We've got two centimeters right here. We're supposed to figure out what the electric flux is through each side of the cube. So let's go ahead and visualize what's going on here. First, we're going to draw the normal vectors for each one of those sides. So the top one has a normal vector like this. This one has one that goes sort of like outwards like this. Think one has one to the right, one's got one to the left, and then there is a bottom one that's going to point downward. And there's going to be a back one sort of on the backside of the cube. Anyway, each one of these surfaces now may or may not have an electric field that goes through it, so we know we're going to have to calculate the electric flux for all of these. So just remember that it's EAcosθ for the electric flux.

Clearly, we can see that for the right side, there is definitely going to be some electric flux here. So the right side is just going to be EAcosθ. But in this case, we have the EA. The cosine of the angle is just going to be zero. So this is just going to be EA. Whereas on the other side, we could make the opposite argument that you have the same exact area because it's a cube. Except in this case, the flux on the left side is just going to be EAcosπ. So it's going to be equal to negative EA.

Now, let's see what's going on for the top side. You have an electric field that points in one direction, and you have a normal vector that points upward. That means that the cosine of this angle right here that it makes is equal to zero. So that means that over here the flux at the top is just equal to zero. By the same reasoning, the flux at the bottom is also equal to zero.

Now, the only two remaining are the front and the back side. So now you have an electric field that points in one direction, and now you have a normal that points straight out, as if I was pointing directly at you. So this angle is also still 90 degrees, even though it's just a different orientation due to our three-dimensional coordinate system. So that means the flux on the front, which, by the way, is going to be equal to the flux on the backside because this is symmetrical, is also going to be equal to zero.

So in other words, we have found that the front, the back, the bottom, and the top are all equal to zero, and the only two surfaces that actually have non-zero flux going through them are going to be the left and the right side. So let's see, we've got 100 Newtons per Coulomb and now we have a side length of two centimeters. So the area over here is equal to two centimeters times two centimeters. That's going to be four square centimeters. But you have to be careful because any time you want to convert this to meters, you have to actually adjust the decimal place two times because you have to do this conversion four times. So this is actually going to be 0.0004 metres squared.

The electric flux is going to be negative 0.04 on the left side and a positive 0.04 on the right side, as if it's just going to be the positive of the negative value on the left side. Those are the fluxes for each one of these sides. Let me know if you guys have any questions.