# Triple integral and charge density

1. Sep 10, 2008

### Dan7620

Alright guys Im looking for some help with this problem regarding calculating total electric charge in a layer of ions. This layer of ions is bounded between the planes x+2y+2z=4 and x+3y+3z=3, and by the 3 co-ordinate planes. The density of the ions is rises linearly from zero at the outer plane ( x+2y+2z=4) and increases linearly to 10^15 at the inner plane (x+3y+3z=4). Furthermore, the surface charge density is constant in planes parallel to the planes x+2y+2z=4 and x+3y+3z=4.

I see that in order to calculate the total electric charge I must compute a triple integral of the charge density, however I'm trying to find an expression for the charge density function. Could anybody help me with writing density (as a function of x,y,z) based upon the information given in the first paragraph? Not looking for the final answer here, just some instruction. Thank you :)

PS. I wasn't sure whether this should be posted here or in the electrical section, sorry just in case.

2. Sep 10, 2008

### Dan7620

EDIT: the second plane, x+3y+3z=3 is incorrect, as it is not parallel to the first one, x+2y+2z=4 (it should be).

3. Sep 11, 2008

### Defennder

As you have said, the two planes aren't parallel, and the boundaries of the required volume isn't specified. If the two planes are suppposed to be parallel, you don't have to resort to fancy triple integration to find total charge. Just find the perpendicular distance between the 2 plane, and then you can easily do an integration in one variable to find the charge stored in a volume element Adx, where dx is an incremental thickness.

4. Sep 11, 2008

### Defennder

Should have rewritten it as the integral: $$\int^{x_2}_{x_1} \lambda (x) A dx$$ where $$\lambda$$ is the total charge per infinitesimal sheet between the 2 planes.

5. Sep 11, 2008

### Dan7620

Ah ok, thanks alot, much simpler.

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