# Integrating dq to find that q(r) = Q(1-e^(-r/R))

1. Sep 16, 2009

### jk0921

1. The problem statement, all variables and given/known data
provided with data that
dq = rho(r) *4phi*r^2*dr
rho(r) = [Q*e^(-r/R) / 4phi R *r^2)

I have to show that the charge q(r) enclosed in a sphere of radius r is q(r) = Q(1-e^(-r/R)) by using appropriate integral. how the integral should be?

2. Relevant equations

3. The attempt at a solution
I've tried to integrate dq = ... but I can't find the final answer that q(r) = Q(1-e^(-r/R))

2. Sep 16, 2009

### gabbagabbahey

It is a pretty straightforward integration. Why not post what you've tried so we can see where you are going wrong?

3. Sep 17, 2009

### iceberg123

never mind

4. Sep 17, 2009

### saunderson

The easiest way is to integrate the charge density in a fitted coordinate system!

Cause you need
$$Q(r) = \int \limits_{\mathcal{V}} \, d^3r \, \rho(r)$$​
of a sphere, the most suitable one is the spherical coordinate system. So you need the volume element
$$d^3r = \rm{?}$$​
and perform the integration!

PS:
In the statement
$$dq = 4\pi \, r^2 \,\rho(r) \cdot dr$$​
two integrations are already perfomed, so the best way to undestand it completley is to do it like i've said above!