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## Homework Statement

A Non-Uniform but spherically symmetric charge distribution has a charge density:

[itex] \rho(r)=\rho_0(1-\frac{r}{R}) [/itex] for [itex] r\le R[/itex]

[itex] \rho(r)=0 [/itex] for [itex] r > R[/itex]

where [itex] \rho = \frac{3Q}{\pi R^3} [/itex] is a positive constant

**Show that the total charge contained in this charge distribution is Q**

## Homework Equations

[itex]Q_{total} = \int \rho(r)dV [/itex] with limits 0 and R

[itex]dV = 4 \pi r^2 dr [/itex]

## The Attempt at a Solution

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I have tried so many solutions it is driving me insane.

Is my dv wrong?

my main method is substituting [itex] \rho_0 [/itex] in and then trying to take the constants out of the integral but then I'm stuck with r^3/R or something like that...

This is a 4 mark question, so that usually indicates it's a 4 step process, but this is taking me many steps to get even close..

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