Question

A flat surface with area 0.14m^2 lies in the x-y plane, in a uniform electric field given by E = 5.1î + 2.1j + 3.5k (kN/C). Find the flux through this surface.

Answer 1

I think I have to use the form of electric flux given by...

\[\phi _{E} = EA \cos \theta \]
but I'm not sure how to approach this with respect to the unit vector relationship! I've never worked with 3–D physics before this particular problem, and I'm not quite sure how to resolve the electric field to solve for the flux.

Can someone help me out?

Answer 2

The equation for electric flux is also given using the dot product
\[\Phi_E = \textbf E \cdot \textbf A\]
Where E is the electric field and
\[\textbf A = A \ \hat{\textbf n}\]
the "area vector" having magnitude A and pointing in the normal direction



Luckily for this problem, we know that since the area is purely in the xy plane the normal vector is along the z axis, so we can say for this problem
\[A \ \hat{\textbf n}=A \ \hat{\textbf k}\]

And the flux is then the dot product

\[\Phi_E = \textbf E \cdot \hat{\textbf k} \ A=(E_i)(0)+(E_j)(0)+(E_k)(A)=.49 \ kNm^2/C\]

^_^