Expression for Electric Field Outside Sphere

[Ryan129]

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.

 

[SammyS]

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.