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## Homework Statement

A distribution of charge with spherical symmetry has volumetric density given by: $$ \rho(r) = \rho_0 e^{ \frac {-r} {a} }, \left( 0 \leq r < \infty \right); $$

where ##\rho_0## and ##a## is constant.

a) Find the total charge

b) Find ##\vec E## in an arbitrary point

## Homework Equations

I've already found the answer of a): ## Q_t = 8\pi a^3 \rho_0##

## The Attempt at a Solution

To solve b), I've used the Gauss law (spherical symmetry) and that's what I've found $$ \vec E = \frac {4\pi a^3 \rho_0} {r^2} \vec r .$$

This answer seems to me very acceptable, but I've looked at the solutionary and there's another result pretty much complicated. What do you think?