Electrostats

Consider a horizontal charged disk with center $O$ and having surface charge density $\sigma$, and radius $R$, Consider a vertical rectangle of dimensions $2a \times 2h$, which cuts the disk at a distance $a$ from its center, such that half of rectangle lies below the disk and half of it lies above the disk.Use $a << R$ to find the value of flux of electric field in $N m^2 C^{-1}$ through the rectangle to the nearest integer. The top view is shown below:

Details and assumptions

$\sigma = 1.05 \times 10^{-4} Cm^{-2}$

$R = 3m$

$a = 2 mm$

$h = 1m$