Expression for Electric Field Outside Sphere

[eric11201120]

Homework Statement

The charge desnsity within a 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.

Relevant Equations

Electric Field outside a sphere
E = KQ/r2
Electric flux
ΦE=∫EdA

I'm not quite sure where to start. If someone could help me I would very much appreciate it.

 

[Doc Al]

Hint 1: What does Gauss's law tell you?
Hint 2: Given that expression for charge density, what's the total charge within the sphere?

 

[Steve4Physics]

Hi @eric11201120. Welcome to PF.

Thee rules (see https://www.physicsforums.com/threads/homework-help-guidelines-for-students-and-helpers.686781/) require you to make some sort of effort before we can help you.

But there seems to be a mistake in the question. The sphere can't be both 'uniformly charged' and have a charge density which is a function of r. That doesn't make sense. What do you think is intended?

 

[Doc Al]

But there seems to be a mistake in the question. The sphere can't be both 'uniformly charged' and have a charge density which is a function of r.

Yes, a very sloppily worded question!