A point charge ‘q’ is placed at a distance ‘ℓ ’ (on the y-axis) vertically above the semi infinite plane surface which lies in the xz plane as shown in the figure. The magnitude of flux of electric field passing through the surface is x q48 ∈0  where x is a positive integer. Find x ?

ϕ=ϕOAB+ϕABCD =q48ε0+q48ε0=q24ε0Imagine a cuboid as shown. Flux through left and right face is zero, as electric filed at infinity is zero.ϕcuboid=qε0∴ϕface=q4ε0⇒ϕOABC=q16ε0Imagine a cube as shown.ϕcube=qε0∴ϕface=q6ε0⇒ϕOAED=q24ε0⇒ϕOAE=q48ε0Hence,ϕshaded region=ϕOABC−ϕOAE=q16ε0−q48ε0=2q48ε0