a nonconducting spherical shell, of inner radius a = 20.4 cm and outer radius b

Question

a nonconducting spherical shell, of inner radius a = 20.4 cm and outer radius b = 25.4 cm, has a volume charge density ? = A/r (within its thickness), where A is a constant and r is the distance from the center of the shell. In addition, a point charge q = 6.00×10-5 C is located at the center.

What value should A have if the electric field in the shell (a < r < b) is to be uniform? (Hint : The constant A depends on a but not on b.)
I got this answer by A=q/(2(pi)(a^3))
A=2.29×10-4 C/m^2
But I can't seem to get part B:

What is the value of E?

Explanation / Answer

i don't know how you got A=q/(2(pi)(a^3))

solution:
take a gaussian surface of sphere of r such that b>r>a
then charge inside the surface=

Qin=q+ charge in the sphere in volume 4/3*pi*r3-4/3*pi*a3

=>Qin=q+ integral of charge

integral of charge= integral {(A/r)*(4r2) r}ra =integral {(4Ar) r}ra

= {(2Ar2) }ra

= 2Ar2 -2Aa2

Qin=q+ 2Ar2 -2Aa2

as E=Qin/(*surface area)

as surface area 4r2

E=q/4r2+ A/2-Aa2/2r2 a<r<b

as E is a constant in a<r<b

=>q/4r2-Aa2/2r2=0 as A/2 is a constant and rest is dependent on r

A=q/2a2

and for r<a

Qin=q

E= q/4r2 no other charge inside

for r>b

Qin=q+ 2Ab2 -2Aa2

E=q/4r2+ A(b2-a2)/2r2

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