1. The problem statement, all variables and given/known data A very long cylinder of radius 2.00 cm has a uniform charge density of 1.50 nC/m. Taking the reference level for the zero of potential to be the surface of the cylinder, find the radius of equipotential surfaces having potentials of 10.0 V, 20.0 V, and 30.0 V. 2. Relevant equations Va - vb = ∫E * dr Lower limit: a Upper limit: b λ = 1.50 nC/m 3. The attempt at a solution I have solved, using Gauss' Law, the electric field of this cylinder. E = λ/(2[itex]\pi[/itex]ε0)(r) Now to integrate, I removed the λ/(2[itex]\pi[/itex]ε0) factor out of the integrand and did this: Vr - V.02 cm = λ/(2[itex]\pi[/itex]ε0) * ∫(1/r)dr Lower limit for this integral: r (the distance from the axis of the cylinder) Upper limit for this integral: 2.00 cm (the radius of the cylinder) So Vr - V.02 cm = Vr =(λ/(2[itex]\pi[/itex]ε0) * ln(.02/r) Since the first part of the problem states that the potential difference is 10 V, I plugged 10 V in for Vr and just solved for r, since that should be the equipotential surface radius. I retrieved an answer of 1.38 cm, but this is incorrect. I can't seem to find my error. Thanks in advance. The correct answer is 2.90 cm.