# Gauss Law

1. Feb 17, 2013

### Pruddy

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

-38.0 nC of charge is uniformly distributed throughout a spherical volume of radius 34.0 cm.
How much charge is contained in a region of radius 23.0 cm concentric with the charge distribution?

2. Relevant equations

Charge density = λ/area

3. The attempt at a solution

I don't know how to approach this problem. I dont know if it is right to use gaus's law.Please if anyone can give me directions or what topic in physics this problem comes from, I will gladly appreciate. Thanks

2. Feb 17, 2013

### tiny-tim

Hi Pruddy!
You're told that the distribution is uniform, so this is just geometry

"-38.0 kg of cheese is uniformly distributed throughout a spherical volume of radius 34.0 cm.
How much cheese is contained in a region of radius 23.0 cm concentric with the cheese distribution?"

3. Feb 17, 2013

### Pruddy

Tiny-Tim,
So am I to used the Electric flux formula to solve this problem? But the question is looking for how much charge?

4. Feb 17, 2013

### ap123

This question has nothing to do with the Gauss's Law or electric flux ( since it doesn't mention the electric field ).

As pointed out in post #2, this is a geometry problem.

Imagine starting with your sphere and removing a section with radius 23cm.
What is the relation between the removed part and the whole sphere?

5. Feb 17, 2013

### Staff: Mentor

What you need is charge density ρ = Q/volume.

How does the total volume (radius 34 cm) compare to the volume of the region (radius 23 cm)?

6. Feb 17, 2013

### whynot314

Set up a Ratio, $\frac{-38nc}{V_{1}}$=$\frac{Q_{2}}{V_{2}}$

7. Feb 17, 2013

### Pruddy

Hi, whynot314.
I used the formular and this are my calculations:

q2 = -38 x 10^(-9)/4*pi*r(0.34)^2 = q2/(4*pi*r(0.23)^2

= -38 x 10^(-9)*4*pi*r(0.23)^2 /(4*pi*r(0.34)^2
= -2.293 x 10^(-9)
I dont know if this is right...

8. Feb 17, 2013

### Dick

You should be using volumes, not surface areas. This isn't a Gauss' law problem. It's a charge density problem. The volume of a sphere of radius r is (4/3)pi*r^3. But even using area the numbers still don't come out the way you say they do.

Last edited: Feb 17, 2013
9. Feb 17, 2013

### Pruddy

Hi, whynot314,
Thanks a lot! You are the best.

10. Feb 17, 2013

### Pruddy

Hi, whynot314,
I got it now.

11. Feb 18, 2013

### whynot314

I am studying this stuff right now to so this problem helped me as well.

12. Feb 18, 2013

### Pruddy

wow. That's awesome!