Collge Physics question, What did I do wrong?

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Collge Physics question, What did I do wrong?



A solid nonconducting sphere of radius r0 has a total charge Q which is distributed according to ρE=br, where ρE is the charge per unit volume, or charge density (C/m3), and b is a constant. 

Determine b in terms of Q. 
My first attempt Attempt: 
b = ρE/r 
b = Q / r(V) 
b = Q / r0(4/3pi r0^3) 
b = 3Q/4pi r0^4 

It is wrong and the explanation told me 
Your answer either contains an incorrect numerical multiplier or is missing one. 

The second time I notice that it is r, but not r0 in ρE=br 
so I changed to 3Q/4pi*r0^3*r 
The correct answer does not depend on: r. As it says 

So what exactly I did wrong? 

part B of this question is 
Determine the electric field at points inside the sphere. 
Using the gauss's law 
I got Q*r / 4pi*e0*r0^3 , e0 means epsilon0 or 8.85*10^-12 
So what is my mistake?



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Posted Answers:

This is a calculus problem. 
ρE = b*r 

The problem is I'm not sure exactly how to solve it. 

I believe that 
Q = ∫ ρE dV 
and that 
dV = 4πr² dr → from V = 4πr³/3 & take the derivative w/r/t r 
so that 
Q = ∫ br * 4πr² dr = 4πb * ∫ r³ dr = πbr⁴ 
evaluated for 0 ≤ r ≤ râ‚€, which means that 
Q = πbr₀⁴ 

Therefore b = Q / πr₀⁴ â—„ 

Try that!