A solid non conducting sphere

[Liquidxlax]

Homework Statement

A solid nonconducting sphere of radius R carries a nonuniform charge distribution, with a charge density ρ = ρ_sr/R, where ρ_s is a constant and r the distance from the centre of the sphere. Show that

i) the total charge on the sphere is

Q= πρ_sR³

and

ii) the electric field inside the sphere is given by

(kQr²)/R⁴

Homework Equations

Q_enc = integral(dQ) = inetgral(ρdV) = ρintegral(dV) = ρV =

((Q4πr³)/3) / ((4πR³)/3) = Q(r/R)³

The Attempt at a Solution

dA = 4πR²dr

ρdA = 4πρ_srRdr

integrate r from 0 to R but i have a 2 in front.

 

[vela]

You're confusing r and R when setting up your integral.

 

[Liquidxlax]

You're confusing r and R when setting up your integral.

even when i do it that way, I'm left with 2 in front and then R^2

 

[Liquidxlax]

i really need help with this one. my prof is fluffing everyone off.

please and thanks :)

 

[vela]

Show your work. I'm not sure exactly what you did.