# Gauss Law

1. Homework Statement

-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?

## Homework Equations

Charge density = λ/area

## 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

tiny-tim
Homework Helper
Hi Pruddy!
-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?

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?"

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

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?

Doc Al
Mentor
Charge density = λ/area
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)?

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

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...

Dick
Homework Helper
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...

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

Hi, whynot314,
I got it now.

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

wow. That's awesome!