Electric Flux on the surface of a sphere

[NWNINA]

Homework Statement

I'm trying to figure out an equation for finding the net flux that abandons the surface of a sphere which contains a line charge distribution an a charge density. The problem is:

A line charge distribution of 0.6m long with a charge density equal to 5C/m, is contained inside a sphere with radius of 5m. Find the net flux that abandons the surface of the sphere.

Homework Equations

What I have done is the following
ψ=DA
D= εE
ψ=εEA=ε(ρ/(2∏εr)(4∏r^2)
∴ψ =2 ρ r

The Attempt at a Solution

ψ= 2(5C/m)(5m) = 50C

I really don't know if this is the correct approach. Any help would be great.

 

[NWNINA]

So I've decided to take a different approach
ψ= ∫∫∫ ρ rdrd∅dθ
not sure if i should use d∅ or dz. maybe the first one because it is spherical.
what limits should I use?

 

[SammyS]

Homework Statement

Im trying to figure out an equation for finding the net flux that abandons the surface of a sphere which contains a line charge distribution an a charge density. The problem is:

A line charge distribution of 0.6m long with a charge density equal to 5C/m, is contained inside a sphere with radius of 5m. Find the net flux that abandons the surface of the sphere.

Homework Equations

What I have done is the following
ψ=DA
D= εE
ψ=εEA=ε(ρ/(2∏εr)(4∏r^2)
∴ψ =2 ρ r

The Attempt at a Solution

ψ= 2(5C/m)(5m) = 50C

I really don't know if this is the correct approach. Any help would be great.

Use Gauss's Law.

Calculating the flux directly by means of a surface integral will be a mess.