(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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?

2. Relevant equations

Gauss's Law: ∫EdA=Q_{encl}/ ε_{0}

Charge density = Q/V

Volume of a sphere = 4/3ϖR^{3}

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?

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# Electric field of a non-conducting sphere

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