# Question about problem solving approach to Gauss' Law

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1. Jun 1, 2016

### RoboNerd

1. The problem statement, all variables and given/known data

Hi, I am studying gauss's law via this book below.

http://faculty.polytechnic.org/cfle...2_web_pdfs_2010/i-Ch14-PCALC--GAUSS'S LAW.pdf

On page 8, and 9, the book describes the shell method of finding the volume of the sphere and then using the area charge density to find the charge.

I tried it a different method:

volume of a sphere is (4/3) * PI * R^3, so I wrote that the volume was (4/3) * PI * (r-R1)^3.
This makes sense to me: I take the volume of the larger sphere and subtract the volume of the smaller sphere with radiuses "r" and "R1" accordingly.

Could anyone please explain to me why my method is wrong, as I got a totally different answer?

Thank you!!

2. Relevant equations

gauss's law
3. The attempt at a solution

attempt is recorded above

2. Jun 1, 2016

### RoboNerd

is it because of the linear function of the charge density?

3. Jun 2, 2016

### haruspex

That does not give you the difference in volume between two spheres. It gives you the volume of a sphere of radius r-R1.

4. Jun 2, 2016

### RoboNerd

ohh I should have done

(4/3) * PI * (r)^3 -
(4/3) * PI * (R1)^3.

yes?

5. Jun 2, 2016

Yes.

6. Jun 8, 2016

### RoboNerd

So why could I have not done the first method? Why is it wrong?

7. Jun 9, 2016

### haruspex

Because (x-y)3 is not the same as x3-y3.

8. Jun 9, 2016

OK, thanks!