Answer to Question #226490 in Electricity and Magnetism for Paulinus

Question

An electric field is generated in between two parallel hundred square meter electrodes that are separated by a distance of 2 centimeters.
We have the one plate charged to 5.0 nano coulomb and the other one. Exactly equal but opposite.

An additional square shaped surface is placed in between plates

Answer 1

An electric field is generated in between two parallel hundred-square-centimetre electrodes that are separated by a distance of 2 cm. We have the one plate charged to 5.0 nano-Coulombs and the other one exactly equal but opposite. An additional "square-shaped" surface ( with side length of a centimetre) is placed in between the plates and rotated such that it makes an angle of pi/4 radians with the electric field. Determine the flux of the electric field through the square surface.

The flux is:

$\Phi=ES'\cos \theta,~(S'=1~cm^2),$

the electric field is:

$E=\frac Ud=\frac q{Cd}=\frac{qd}{d\varepsilon_0 S}=\frac q{\varepsilon_0 S},~(S=100~cm^2,~q=q_1-q_2=5-(-5)=10~nC),$

so the flux is:

$\Phi=\frac{qS'}{\varepsilon_0 S}\cos \theta=8~\text{V}\cdot \text{m}.$