An infinitely long uniformly charged non-conducting cylinder has radius R and volume charge density ρ.The maximum electric-field magnitude produced by this charge distribution is:
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An infinitely long uniformly charged non-conducting cylinder has radius R and volume charge density ρ.The maximum electric-field magnitude produced by this charge distribution is:

G1 Physics · Accepted Answer

Inside, E(x) = ρx/(2ε₀), so E increases linearly. Outside, E(x) = ρR²/(2ε₀x), so E decreases as 1/x. Hence the maximum occurs at x=R: E m a x E_max E m ​ a x = ρR/(2ε₀).