Electric Flux and Gauss's Law (Please Help)

Question

A long straight wire has a charge per unit length of 3.00 x 10^-12C/m. At what distance from the wire is the electric field equal to 0.600N/C?

Answer 1

If you are using a Gaussian surface (a long cylinder of radius R (which we want to solve for) and length, L, and make the assumption that E is purely radial, Gauss's Law states that

EA = Q_enc/ε_o For the uniform E field around the wire

A = 2πRL Q_enc = λL where λ is the charge per length of wire. and ε₀ is the electrical permittivity of free space.

E(2πRL) = λL/ε_o

Rearranging t solve for R:

R = λ/(2πRε_o) and plug in the givens in appropriate SI units.

Answer 2

E = q/(2πε₀r); r = q/(2πε₀E) = 3·10^-12C/m/2π·8.854·10^-12F·m·0.600N/C) = 0.090 m