# Gauss's Law and electric flux

rambo5330
Can someone please help me work through this problem I've spent over an hour on this trying to figure out what to do.. here's the question

A nonuniform electric field is given by the expression E = ay^i + bz^j + cx^k,
where a, b, and c are constants. Determine the electric flux through a rectangular
surface in the xy plane, extending from x = 0 to x = w and from y = 0 to y = h.

this question can be viewed better here http://web.uvic.ca/~jalexndr/week%203%20problems.pdf (question #54)

i basically use gauss's law and get it down to something like

= C$$\int$$ (x dA )

my method here was two take the dot product of the electric field and dA which is said to be perpendicular to the surface in the x y plane therefore it will act along the z axis
so this dot product comes out equalling cxdA where c is a constant.... where do i go from here.. the answer is given as (1/2 chw^2)

chronos98
You have the right answer. To evaluate your expression, use dA = dxdy, so now you have $$\int\int{x*dxdy}$$ with x going from 0 to w, and y going from 0 to h. If you go through the steps, you will get the same answer.

rambo5330
Oh excellent, so judging by what you wrote to continue past where I left off it involves a double integral? if this is the case I have not learned the double integral yet this semester which makes more sense why I as so stuck ..

chronos98
well, this case does not have variables x or y in the limits. do the definite integrals separately and just multiple the results together. so it'll be like this $$c*\int_{0}^{w}xdx*\int_{0}^{h}dy$$

cupid.callin
Your surface is in XY plane
flux due to field in i and j derection is 0

only k left, which i assume is easy!!!