[Electrostatics] Flux Problem,

[ERTW]

Electrostatics Flux Problem

Homework Statement

A linear charge rho L = 2.0 uC lies on the y-z plane. Find the electric flux passing through the plane extending from 0 to 1.0m in the x direction and from -infinity to infinity in the y direction.

Homework Equations

Alright, so the formula to use is:

flux = (integral(integral)(Ds * dS)) where dS is a vector whose direction is normal to the surface element ds and has a magnitude of ds and Ds is the electric flux density passing through ds

Turns out the answer is simply 1/8 * the given line charge.

This is because the lines x = 0 and x = 1 when viewed from above make a 45 degree angle. The area enclosed here is exactly 1/8th of the entire area.

A more analytical solution would be great though.

 

[BigJDubs]

The Attempt at a SolutionA more analytical solution would be to use the formula above. Start off with the double integral of electric flux density over the given area and solve for the flux:Flux = (integral(integral)(Ds * dS)) = (integral(integral)(rho/epsilon_0) * dS) = (integral(integral)(2.0 uC/8.85e-12 C^2/Nm^2 ) * dS) = (1/8) * (2.0 uC) = 0.25 uC