Determine and draw the graph of electric field due to infinitely large non-conducting sheet of thickness t and uniform volume charge density `rho` as a function of distance x from its symmetry plane.
(a) `x lt t/2` (b) `x ge t/2`

Explanation

We can consider two sheets of thickness `(t/2-x)` and `(t/2+x)`
Where the point P lies inside the sheet.
Now, net electric feld at point P :

`E=E_(1)-E_(2) =Q_(1)/(2 A epsi_(0)) -Q_(2)/(2 a epsi_(0)) [Q_(1)" : Charge of left sheet, "Q_(2)" : charge of right sheet."]`
`=(A rho(t/2+x)- rhoA (t/2-x))/(2 A epsi_(0))=(rho x)/epsi_(0)`
For point which lies outside the sheet we can consider a complete sheet of thickness t

`E=(sigma t A)/(2 a epsi_(0))=(sigma t)/(2 epsi_(0))`
Alternate : We can assume thick sheet to be made of large number of uniformly charged thin sheets. Consider an elementary thin sheet of width dx at a distance x from symmetry plane.
charge in sheet `= rho Adx` (A : assumed area of sheet)
surface charge density, `sigma=(rho A dx)/(A)`
So, electric field intensity due to elementary sheet : `dE=(rho dx)/(2 epsi_(0))`
(a) When `x lt t/2 rArr" "E_("Net")= underset(-t//2)overset(x)(int) (rho dx)/(2 epsi_(0)) - underset(x)overset(t//2)(int) (rho dx)/(2 epsi_(0))=(rho x)/epsi_(0)`
(b) When `x gt t/2 implies" "E_("Net")= underset(-t//2)overset(t//2)(int) (rho dx)/(2 epsi_(0))= (rho t)/(2 epsi_(0))`