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**1. Homework Statement**

I'm having a bit of trouble with this problem:

"A spherical ball of charge has radius R and total charge Q. The electric field strength inside the ball (r≤R) is E(r)=r^4Emax/R^4.

a. What is Emax in terms of Q and R?

b. Find an expression for the volume charge density ρ(r) inside the ball as a function of r."

**2. Homework Equations**

Φ=EA

Φ=Q/ε0

Q=ρV

E(r)=r^4Emax/R^4

**3. The Attempt at a Solution**

I found the answer for part (a.) with no trouble:

Emax=Q/(4πR^2ε0)

However, part (b) has proved to be a lot harder. Here is my attempt:

Since φ=EA and φ=Q/ε0,, I chose to use the original equation for electric field (since I have a correct answer for Emax), multiply it by the surface area of a smaller sphere with radius "r" (inside the original sphere with radius R), and set this equal to Q/ε0 as follows:

Q/ε0=(4πr^2)(r^4Emax/R^4)

Then, I determined the charge of the small sphere with radius "r" (inside the original sphere with radius R) as follows:

ρ=charge density

Q=ρV

Find charge of small sphere (inside the original sphere with radius R):

dQ=ρ4πr^2dr

Q=∫ρ4πr^2dr (with the limits of the integral being 0 to r)

Q=(4/3)πr^3ρ

Then I used the equation I found earlier:

Q/ε0=(4πr^2)(r^4Emax/R^4)

Then I input the values for Emax and Q, and I get the formula for charge density:

(4/3)πr^3ρ/ε0=r^4(Q/4πR^2ε0)/R^4

ρ(r)=3r^3Q/4πR^6

I tried entering the value to see if it is correct and the program tells me that I am missing or failing to add a numerical value. I've tried going through it and I can't seem to find the error. If one of you all can help me out I'd be grateful.