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

b.

explanation:

the working equation for the angular size is the product of the physical size and 360 degrees divided by the product of two pi and distance from earth. the minimum size would be 0.559 degrees while the maximum size would be 0.49 degrees.