# Expression for Electric Field Outside Sphere

## Homework Statement

The charge desnsity within a uniformly charged sphere of radius R is ρ = ρ0 - ar2, where ρ0 and a are constants and r is the distance from the center. Find an expression for a such that the electric field outside the sphere is zero.

## Homework Equations

Electric Field outside a sphere
E = KQ/r2

## The Attempt at a Solution

I'm having trouble setting up this problem, I'm not quite sure where to start. If someone could help me I would very much appreciate it.

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## Homework Statement

The charge desnsity within a uniformly charged sphere of radius R is ρ = ρ0 - ar2, where ρ0 and a are constants and r is the distance from the center. Find an expression for a such that the electric field outside the sphere is zero.

## Homework Equations

Electric Field outside a sphere
E = KQ/r2

## The Attempt at a Solution

I'm having trouble setting up this problem, I'm not quite sure where to start. If someone could help me I would very much appreciate it.
Hello Ryan129. Welcome to PF !

You will need to integrate the charge density over the whole volume of the sphere & use Gauss's Law to tell you haow muck total charge you need to get that E-field outside of the sphere.

There are other ways to do it.