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

 

[Nate810]

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

 

[ogb p]

I would like to provide a response to your inquiry. First, let me explain the concept of electric flux. Electric flux is a measure of the amount of electric field passing through a given area. It is represented by the symbol ΦE and is calculated by taking the dot product of the electric field vector and the surface area vector.

In your problem, you have a uniform line charge with a linear charge density of 6nC/m situated on the x-axis. The electric flux per unit length passing through a plane strip extending in the x direction can be calculated by taking the integral of the electric field over the surface of the strip.

To solve this problem, we need to first determine the electric field at any point on the strip. Since the line charge is uniform, the electric field will also be uniform and will be directed towards or away from the line charge, depending on the sign of the charge.

Next, we need to calculate the surface area of the strip. Since the strip extends in the x direction, the surface area will be equal to the length of the strip (in this case, y=1 and z=5) multiplied by the width of the strip (in this case, the width is infinitesimally small since it is a line).

Now, we can use the formula for electric flux to calculate the flux per unit length passing through the strip. The integral of the electric field over the surface of the strip can be simplified to the product of the electric field and the surface area, since the electric field is uniform.

Substituting the values given in the problem, we get:

ΦE = (6nC/m)(1m)(0.0001m) = 0.0006 nC/m

Therefore, the electric flux per unit length passing through the plane strip is 0.0006 nC/m. I believe the answer you provided (1.31 nC/m) may be incorrect. I hope this explanation helps you understand the concept of electric flux and how to solve this type of problem. If you have any further questions, please don't hesitate to ask.