The electric flux through this plane is equal to the electric flux through the surface of the spherical cap.

Height of spherical cap h= a( 1-√2/2)

So the spherical cap area S= 2πa? (2-√2)/2=πa？ (2-√2)

Ratio of spherical crown area to spherical surface area

k= S/4πa？ = (2-√2)/4

Therefore, the electric flux through the spherical cap is (2-√2)Q/4ε0.