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## Homework Statement

A solid non-conducting sphere of radius R carries a uniform charge density. At a radial distance r

_{1}= R/4 the electric field has a magnitude Eo. What is the magnitude of the electric field at a radial distance r

_{2}=2R?

## Homework Equations

Gauss's Law: ∫EdA=Q

_{encl}/ ε

_{0}

Charge density = Q/V

Volume of a sphere = 4/3ϖR

^{3}

## The Attempt at a Solution

For R/4: ∫EdA=Q

_{encl}/ ε

_{0}= 1/(4ϖε

_{0})(Q/R

^{3}) (R/4) = E

_{0}

for 2R: ∫EdA=Q

_{encl}/ ε

_{0}= 1/(4ϖε

_{0})(Q/ [2R]

^{2})

So for R/4, it simplifies to 1/(4ϖε

_{0})(Q/4R

^{2}). I know the answer is E

_{0}so i guess 2R simplifies to 1/(4ϖε

_{0})(Q/ 4R

^{2}) and everything cancels to leave E

_{0}.

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?