How Do You Calculate Electric Flux Through a Circular Disk in an Electric Field?

[Physicus2]

Homework Statement

"Given a constant electric field E = E(subscript 0)(1 / square root of 2 i + 1 / square root of 2 k), find the electric flux through a circular disk of radius a lying flat in the x-y plane. Orient the disk so that the positive direction is toward positive z.

Homework Equations

The most relevant equation to this problem is Eflux = integral of E dot dA.

The Attempt at a Solution

I've completely finished a solution, but there are many places to make mistakes here, I think, despite what may be a simple problem.

I said that Eflux = (-E subscript 0) double integral from 0 to a (x and y) of E dot k dx dy. I went on to place 1 / square root of 2 into the integral, but only once for the k and not the i component. Would this be correct? I then integrated with respect to x and got (1 / square root of 2)x dy. Integrating again, I think I get (1 / square root of 2)a^2. Note that i replaced x with a there. I'm unsure if I did my double integral correctly...I'm only beginning Calculus 3 now, and it wasn't a prerequisite for Physics. Oh well.

When all is said and done, I get -E(subscript 0) a^2 / square root of 2.

Is my answer close? I presumed that E is negative because the disk was in the positive Z direction. I apologize for the fact that I'm unable to upload images of my work. Any help would be very much appreciated!

 

[mukundpa]

Is the field is uniform?

if no then think of integration.

if yes, no need of integration simply write field and the area as vectors and perform dot product of them.