Find Charge in Sphere: Integrate \rho(r)

[YoGabbaGabba]

Homework Statement

In a sphere of radius R, the charge density varies as [tex]\rho[/tex](r) = Br^N. There is no charge outside the sphere. B and N are constants.

a.) Find the charge enclosed in a sphere of radius r<R.

Homework Equations

[tex]\rho[/tex]=dq/dv

The Attempt at a Solution

I integrated [tex]\rho[/tex](r)(4[tex]\pi[/tex]r²dr) and got q=(4[tex]\pi[/tex]Br^N+3)/(N+3) + C. Is this right? If so, would it be correct to use the boundary condition; @ r=R, q=0 in order to solve for C? It doesn't sound right because there must be charge at the surface?

 

[rl.bhat]

Hi YoGabbaGabba, welcome to PF,
You are required to find the field at r<R. So you need not the condition r = R. Instead you can take the condition q = 0 at r = 0.

 

[YoGabbaGabba]

Thanks for your time. So if asked to find the charge when r>R, is the charge simply zero or do we consider the boundary conditions r=R? Thanks.

 

[rl.bhat]

Thanks for your time. So if asked to find the charge when r>R, is the charge simply zero or do we consider the boundary conditions r=R? Thanks.

Charge density cannot be zero between r = 0 to r = R. And asking to find the charge density when r > R is meaning less.