A vector field is pointed along the z-axis,
v → = a/(x^2 + y^2)z .
(a) Find the flux of the vector field
through a rectangle in the xy-plane between a < x < b and
c < y < d .
(b) Do the same through a rectangle in the
yz-plane between a < z < b and c < y < d . (Leave your
answer as an integral.)
Φ = E⋅A
E = F/q
The Attempt at a Solution
The problem looks similar to this (I used an image of a similar example):
This example here had flux E0⋅A = E0ab
So for this problem, I tried doing the same thing but first finding electric field of vector v: E = F/q = a/(x^2 + y^2)z / q = aq / (x^2 + y^2)z
And then plugging into formula for Φ:
Φ = E⋅A = aq / (x^2 + y^2)z ⋅ xy
I know I messed up somewhere, especially because the question asks to have an integral for an answer but I'm not sure which formula to use or how to use it.