An infinitely long uniform line charge distribution of charge per unit length λ lies parallel to the y-axis in the y-z plane at z=32a  (see figure). If the magnitude of the flux of the electric field through the rectangular surface ABCD lying in the x-y plane with its centre at the origin is  z=λLnε0 ( ε0 =permittivity of free space), then the value of n  is

Imagine , a cylindrical gaussian surface of length L and radius a.tan∠APO=a23a2=13​⇒∠APO=300​Now , ∠APD=2∠APO=600Given rectangular surface ABCD subscribes an angle  600 at the infinity long uniform line of charge.The total angle subscribe by cylinder is 3600 and charge enclosed is λL.Flux through the rectangle is same as the flux through 16th of the hexagon since it subtends 600 at P and field lines are symmetrically radially outwards.ϕcyl=q∈0​∴ϕABCD=q6∈0=λL6∈0​⇒n=6