How does one do the following Integral.

[Quantumpencil]

Homework Statement

The problem is really not bad; It's to find the flux due to a point charge at the center of Cube of side length d. I've gotten the answer I believe using Gauss's law (q/6epsilon)

I tried doing a Flux integral, and the integral seems kind of a pain in the ***... I'm not sure how to do it. I will post where I'm at and hopefully someone can tell me how to integrate this.

the exact question was

"Find the flux through a face of a cube from a point charge at the cube's center"

Homework Equations

The Attempt at a Solution

First I chose the face, assuming the charge is at the origin, such that da=dzdy(x), x = d/2, and y and z vary from -d/2 to d/2. I then changed Coulombs law to Cartesian coordinates and did some dot products, and substituted in d/2 for x.

\int[\frac{Q(d/2)}{(d^2/4)+y^2+z^2)^{3/2}}dydz

How can one integrate this?

 

[Gokul43201]

Please write down the question exactly as it was given to you. An electric field can not have dimensions of q/epsilon (a flux can). And please be more clear in your working - write full equations instead of fragments. Right now, one can only guess what you are trying to calculate.

 

[Quantumpencil]

Yeah, don't know why I typed Electric field, the problem is to find

\int(E)\cdot da, the flux through the surface.

 

[Dick]

If you already figured out the flux using Gauss' law and symmetry, why do you need to do the painful integral?

 

[Quantumpencil]

I mean, I just usually try to work problems multiple ways. If the integral isn't do-able then I suppose I won't, but often times I just don't think of the proper tricks to solve integrals and things, and doing problems that was as well keeps my bank of problem solving knowledge sharper.

 

[Dick]

I'm sure you probably can do it. But I think the lesson learned would be disproportionate to the effect involved. If it's easy both ways, do it both ways. If it MUCH easier one way stick with that one.