# Calculating flux through a spherical Gaussian sir surface

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 $$x^2 + y^2 + z^2 = 1;\, x>0;\, y>0;\, z>0\quad?$$

My Attempt:

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,

$$\frac{3\lambda}{2\epsilon_0}$$

$$\frac{3\lambda}{4\epsilon_0}$$
where $$\epsilon_0$$ is the permittivity of free space. Any help would be appreciated.
Since there are 8 quadrants in a sphere you'll get answer $$\frac{3\lambda}{4\epsilon_0}$$ I think you're assuming it to have 4 quadrants,Thus you are ending up with $$\frac{3\lambda}{2\epsilon_0}$$