# Problem: The electric field due to an infinite line of charge is perpendicular to the line and has magnitude E= λ/2πε(0). Consider an imaginary cylinder with a radius of r = 0.145 m and a length of l = 0.405 m that has an infinite line of positive charge running along its axis. The charge per unit length on the line is λ= 4.00 μC/m.1. What is the electric flux through the cylinder due to this infinite line of charge? ( φ= ? N•m2/C)2. What is the flux through the cylinder if its radius is increased to r = 0.585 m ? ( φ= ? N•m2/C)3.  What is the flux through the cylinder if its length is increased to l = 0.800 m ? ( φ= ? N•m2/C)

###### FREE Expert Solution

Gauss law:

$\overline{){\mathbf{\phi }}{\mathbf{=}}\frac{{\mathbf{q}}_{\mathbf{e}\mathbf{n}\mathbf{c}}}{{\mathbf{\epsilon }}_{\mathbf{0}}}}$

1.

Flux through the cylinder,

φ = qenc0 = λL/ε0 ###### Problem Details

The electric field due to an infinite line of charge is perpendicular to the line and has magnitude E= λ/2πε(0). Consider an imaginary cylinder with a radius of r = 0.145 m and a length of l = 0.405 m that has an infinite line of positive charge running along its axis. The charge per unit length on the line is λ= 4.00 μC/m.

1. What is the electric flux through the cylinder due to this infinite line of charge? ( φ= ? N•m2/C)

2. What is the flux through the cylinder if its radius is increased to r = 0.585 m ? ( φ= ? N•m2/C)

3.  What is the flux through the cylinder if its length is increased to l = 0.800 m ? ( φ= ? N•m2/C)