Help with linear charge density and flux

[artsakh]

Homework Statement

The y-axis carries a uniform linear charge density of -2 nC/m, and there is a 8 nC point charge
at the point (3 cm, 0 cm, 0 cm) as well as a -4 nC point charge at the point (-8 cm, 0 cm, 0 cm).
What is the electric flux through a closed spherical surface of radius 4 cm centered at the origin?

Homework Equations

I know that flux is 4πkQ_in or Q_in/ε₀, i don't understand where the linear charge density comes in. I know that the 8nC charge would be inside the sphere.

The Attempt at a Solution

I tried adding the linear charge density and the 8nC charge and putting it through that formula but i don't understand how the -4nC charge affects the flux, or how to factor it in.

Any help would be greatly appreciated

 

[artsakh]

The charge outside the sphere doesn't affect the flux, correct? when adding the charges inside the sphere, -2 and 8, which gives 6nC, and putting it through the formula, 4πkQin, i get 678.58, but the correct answer is 886Nm²/C

 

[Nytik]

You are correct that the charge outside the sphere has no influence.
You have made a mistake in determining the charges inside. While there is one charge of 8nC, the 2nC/m is a charge density, not a charge itself.
You need to calculate the amount of charge within the sphere given this charge density, and the radius of the sphere. How might that be accomplished?

 

[artsakh]

well i have the equation E = 2kλ/r. E = k8nC/(.08)²?? but how does that help??

 

[Nytik]

Just think about the charge on the y-axis for a moment.
It has a charge density -2nC/m. The sphere is radius 0.04m, so what is the total charge (on the y-axis) inside the sphere?

Add this to the 8nC charge, and you have your Qin.

 

[artsakh]

im not sure. i don't see how its related at all, i mean besides a volume-density relation

 

[Nytik]

The charge density means that for every metre on the y-axis, there are -2nC of charge present. There is 0.08m of the y-axis within the sphere.
Since charge density = charge/length, you can rearrange this equation to give the charge on the y-axis contained within the sphere.