Electric flux from line charge through plane strip

[Natique]

Hey there! :)

Homework Statement

A uniform line charge with linear charge density = 6nC/m is situated coincident with the x-axis. Find the electric flux per unit length of line passing through a plane strip extending in the x direction with edges at y=1, z=0, and y=1, z=5.
The final answer is 1.31 nC/m. Only problem is I have no idea how to get it.

Homework Equations

integral of D.ds over a closed surface = electric flux = Q enclosed.

The Attempt at a Solution

Attached

I'm sure the answer is really obvious, but I'm just not seeing it. I attached two solutions, but I actually attempted about 6 other ways, all of which are so pathetically illogical I'd really rather not post them. Anyway any help would be reeeeeeeeally appreciated! And it's not a homework question, so it'd be awesome if you could walk me through it step by step.

Edit: Do you think this should be in the advanced physics subforum? :S

 

[member 553083]

Ok, here is a possible solution: We want to calculate the electric flux per unit length through the plane strip extending in the x direction with edges at y=1, z=0, and y=1, z=5. First, we need to calculate the electric field due to the line charge. The electric field at any point (x,y,z) is given by E = (λ/2πε_0)(1/r), where λ is the linear charge density and r is the distance from the line charge to the point. Now, we can calculate the electric flux over the plane strip by integrating the electric field over the area of the strip. The electric flux is given by Φ = ∫ E dA where E is the electric field and dA is the differential area element. Since the electric field does not depend on the coordinates y and z, we can simplify the integral to Φ = ∫ E dx dy dz where x is the variable along the x-axis and y and z are the variables along the y and z directions. Now, using the formula for the electric field, we can rewrite the integral as Φ = (λ/2πε_0) ∫ 1/r dx dy dz Now, we can use the following identities r^2 = x^2 + y^2 + z^2 and 1/r = 1/√(x^2 + y^2 + z^2) to rewrite the integral as Φ = (λ/2πε_0) ∫ 1/(x^2 + y^2 + z^2) dx dy dz Now, we can use the following identity 1/(x^2 + y^2 + z^2) = 1/x ∫ 1/(1 + (y^2 + z^2)/x^2) dx to rewrite the integral as Φ = (λ/2πε_0) ∫ 1/x dx dy dz ∫ 1/(1 + (y^2 + z^2)/x^2

 

[Levi69]

I’m sure someone might’ve solved this by now so did you get the answer?

 

[kuruman]

Please note that this thread is almost 17 years old. It is unlikely that you will get an answer to your query any time soon.

 

[Vanadium 50]

Please note that this thread is almost 17 years old.

It's pre-spam. Better to report it than to engage the spammer.

 

[kuruman]

Done. I wasn't going to engage anyway.

 

[Levi69]

It's pre-spam. Better to report it than to engage the spammer.

Wdym by pre-spam?

 

[berkeman]

Very old thread locked.