Three uniformly charged wires with linear charge density $\lambda$ are placed along $x,y$ and $z$. What is the flux of the electric field through Gaussian surface given by $$x^2 + y^2 + z^2 = 1;\, x>0;\, y>0;\, z>0\quad?$$
The given equation represents a sphere with its center at the origin and radius equal to 1.
Since the given restrictions are $x>0;\, y>0;\, z>0$, I thought calculating the flux through the entire sphere and then dividing by 4 would give us the answer. I calculated the flux as,
But the answer given is,
where $\epsilon_0$ is the permittivity of free space. Any help would be appreciated.