Question about problem solving approach to Gauss' Law

[RoboNerd]

Homework Statement

Hi, I am studying gauss's law via this book below.[/B]
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!

Homework Equations

gauss's law

The Attempt at a Solution

attempt is recorded above[/B]

 

[RoboNerd]

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

 

[haruspex]

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

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

 

[RoboNerd]

ohh I should have done


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

yes?

 

[haruspex]

ohh I should have done


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

yes?

Yes.

 

[RoboNerd]

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

 

[haruspex]

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

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

 

[RoboNerd]

OK, thanks!