- #1

Denver Dang

- 148

- 1

## Homework Statement

You are informed that the charge density is:

[tex]$\rho \left( r \right)=k{{r}^{-n}},r<a$[/tex],

where

*k*is a constant and

*n*is a whole number.

Determine

*n*.

## Homework Equations

Besides that, I know that:

[tex]\[E=\frac{Q}{4\pi {{\varepsilon }_{0}}}\frac{1}{{{r}^{2}}},r<a\][/tex]

(E is spherically distributed btw)

## The Attempt at a Solution

When I have the charge density I know that:

[tex]dQ=4\pi {{r}^{2}}\rho \left( r \right)$[/tex]

So by integrating from 0 to

*a*that I get that:

[tex]Q=\frac{4\pi {{r}^{3-n}}k}{3}$[/tex]

Gauss' Law states (For my case):

[tex]E\left( r \right)\left( 4\pi {{r}^{2}} \right)=\frac{Q}{{{\varepsilon }_{0}}}$[/tex]

So when I put this together I just get the one side equal the other side :S

And I know that

*n*= 1.

What am I doing wrong ?