# Understanding The Electric Flux of A Cube Rotated by an Angle Theta

1. Jan 8, 2014

### mrrocketknigh

Hey, all, so I have been studying this problem all morning, and I do not understand two aspects to this example problem. I included a photo of the diagram used in this problem. You will see two cubes, but the diagram which corresponds to the problem below is the one on the right.

PROBLEM: Find the electric flux through each face of the cube and the total flux of the cube when the cube is turned by an angle theta. View attachment 65421

Below both diagrams in the photo is the answer given; they are the respective fluxes of each side of the cube. What I don't understand is how for n3 the flux is equal to E(L^2)cos(90* + THETA) = - E(L^2)sinTHETA .

I tried finding why the cosine is also equal to the negative sine in this problem, but to no avail. If someone can help me gain a new or more efficient perspective so that I can see the logic of the problem, I would greatly appreciate it. The flux of a uniform electric field, is:
FLUX = E (A*n) cosTHETA. where E is the magnitude of the strength of the electric field, A is the area of the cube, n is the direction of the normal vector to side of the cube, and THETA is the angle the cube was turned ( this I am not completely sure on, if I am wrong then please correct me).

Cheers,

MrRocketKnight

2. Jan 8, 2014