Line of infinite charge and a gaussian sphere

[stunner5000pt]

Construct a spherical gaussian surface centered on an infinite line of charge. Calculate the flux through the sphere and thereby show that it satisfies gauss law.

I know how i can do it for a cylinder, but a sphere?

I know that the ends of the wire (one diameter) wil have zero flux at it's ends

but wouldn't i have to integrate over a big hemispherical surface and then multiply by two but ... wouldn't it be tedious?

 

[Galileo]

but wouldn't i have to integrate over a big hemispherical surface and then multiply by two but ... wouldn't it be tedious?

Yes, but that's probably the reason they're asking you to do it. It shows the power of symmetry in applying Gauss' Law.

 

[Gokul43201]

It's not hard. You know what E(r) is. Take a point at polar angle \theta and find E(r).n in terms of \theta. Integrate over the sphere.