The electric field at 4 cm from the center of a long copper rod of radius 2 cm has a magnitude of 4 n/c and is directed outward from the axis of the rod. (a) how much charge per unit length (in c/m) exists on the copper rod?
(b) what would be the electric flux (in n · m^2/c) through a cube of side 3 cm situated such that the rod passes through opposite sides of the cube perpendicularly?

Explanation:

I will use the Gauss's Law to find the field:

The surface S is an "infinite long" cylinderr of radio r, the normal vector only has radial coordinates (the field too).

The copper is a conductive material, so, it only has a charge distributed on its surface.

Then: E(r)=0 if r<R=2cm

if r>=2cm:

E(4cm) = σ(2x10⁻²m)/((4x10⁻²m)(8.85x10⁻¹²C^2 / (N·m^2))) =

σ 5.64x10⁻¹²Nm^2/C = 4N/C => σ=7.08x10^-13C/m^2

a) A=C/L=σ.2π.R= (7.08x10^-13C/m^2)(2π)(2x10⁻²m) = 8.90x10^-14C/m

b) Based on Law's Gauss we know that the flux only depends of the charge inside the surface, and this cube only encloses 3cm, so, using the previous result: Flux=A*0.03m=2.67*10^-15Nm^2/C

do you have a formula possibly