Answer to Question #224645 in Electricity and Magnetism for Ester N Filippus

Question

QUESTION 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.

Answer 1

$\Phi=ES'\cos \theta,$

$E=\frac Ud=\frac q{Cd}=\frac{qd}{d\varepsilon_0 S}=\frac q{\varepsilon_0 S},$

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