Electric field from spherically symmetric charge distributio

[cookiemnstr510510]

Homework Statement

A spherically symmetric charge distribution produces the electric field E=(200/r)r(hat)N/C, where r is in meters.
a) what is the electric field strength at 10cm?
b)what is the electric flux through a 20cm diameter spherical surface that is concentric with the charge distribution?
c)How much charge is inside this 20cm diameter spherical surface?

Homework Equations

φ_e=∫E⋅dA=Q_enclosed/ε₀

The Attempt at a Solution

question a is pretty straightforward:
a) E=(200/.1m)N/C=2x10³N/C
part b is where I get stuck, here's my attempt:
∫E⋅dA=Q_enclosed/ε₀, Q_enclosed is just some charge distribution so let's say we know it and keep it in its variable form, Q_enclosed.
∫E⋅dA=Q_enclosed/ε₀→EA=Q_enclosed/ε₀
since the 20cm diameter spherical surface we drew is a known shape (spherical) we can use it as a gaussian surface?
E4πr²=Q_enclosed/ε₀→E=KQ_enclosed/r². Clearly I see the problem of having two unknowns here.

I guess the problem says nothing about what the dimensions of the "spherical symmetric charge distribution" is... maybe this comes into play?

Just had an idea:
The problem states what the electric field goes as
so for part b:
E=(200/.1m)N/C, our r for part b is the radius of the 20cm concentric spherical surface is 10cm→.1m
E=2000N/C
Φ_e=EA=2000N/C(4π0.1m²)=251.3Nm²/C

If this is correct then part c should be easy:
φ_e=∫E⋅dA=EA=Q_enclosed/ε₀
we just solved for fluxφ_e
φ_eε₀=Q_enclosed therefore,
Q_enclosed=(251.3Nm²/C)(8.85x10^-12C²/Nm²)=2.24x10^-9C

 

[cookiemnstr510510]

follow up question:
Is there a hint buried somewhere in the problem that should tell me that the electric field should go as E=σ/2ε₀, σ being charge/area?
If so where?
if not should I assume the electric field goes as E=KQ/r²?