A solid non-conducting sphere of radius R carries a uniform charge density. At a radial distance r1= R/4 the electric field has a magnitude Eo. What is the magnitude of the electric field at a radial distance r2=2R?
Gauss's Law: ∫EdA=Qencl / ε0
Charge density = Q/V
Volume of a sphere = 4/3ϖR3
The Attempt at a Solution
For R/4: ∫EdA=Qencl / ε0 = 1/(4ϖε0)(Q/R3) (R/4) = E0
for 2R: ∫EdA=Qencl / ε0 = 1/(4ϖε0)(Q/ [2R]2)
So for R/4, it simplifies to 1/(4ϖε0)(Q/4R2). I know the answer is E0 so i guess 2R simplifies to 1/(4ϖε0)(Q/ 4R2) and everything cancels to leave E0.
However, I feel like I'm lost in the math at this point. If I'm right, could someone explain the math and if I'm wrong could someone just point me in the right direction?