# Jackson Emag 1.

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1. Dec 7, 2016

### IxRxPhysicist

Hey all,
So the question in Jackson 1.4 is that I have 3 spheres that all have a total charge Q on them, but each sphere has different material properties. For instance, I have a conducting sphere, a sphere with a uniform charge distribution, and one with a charge distribution that has a charge distribution that varies as rn. It's the last one I am having trouble with, how can I get an r dependence in ρ without screwing up the units? I tried something like:

ρ(r) ∝ ρo*(rn+1/rn)

buuuuut that still leaves me some messed up units.

Also, ρ0 = 3Q/(4πr3)

Any ideas?

2. Dec 7, 2016

### phyzguy

You can have $\rho(r) = \rho_0 \, r^n$, but the units of $\rho_0$ will not be $\rm \frac{Coulombs}{cm^3}$, they will be $\rm \frac{Coulombs}{cm^{3+n}}$,. And then you have to determine $\rho_0$ by integrating the total charge over the sphere to give Q.

3. Dec 7, 2016

### IxRxPhysicist

Whoa whoa ρ can take on arbitrary units? Like Coulombs/cm3+n? The units just have to balance out in ∫ ρ dV = Q?....Also as an aside, are you using LaTex or something because I like the format in your response.

4. Dec 7, 2016

### phyzguy

Yes, $\rho_0$ is just a constant in your equations that can have whatever units it needs to to make the units come out right. In that case it's not a charge density any more.