- #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 ?