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## Homework Statement

There is a charge density rho that exists in a spherical region of space defined by 0 < r < a.

[tex]\rho (r) = Ke^{-br}[/tex]

How do you find the electric field if a charge density varies as such?

## The Attempt at a Solution

I found Q total = [tex]\int \int \int \rho dV[/tex]

Now I need to find E.

My real question is can I just put Q (as a function of r) into E = kQ/r^2? Or do I need to reevaluate the integral using dq = [tex]\rho r^2 sin(\theta) dr d\theta d\phi[/tex]

I get two different answers, (and I would have thought they should be the same) so which method is correct? I would have thought either would work.

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