An infinitely large non-conducting sheet of thickness t and uniform volume charge density `rho` is given in which left half og the sheet contains charge density `rho` and right half contains charge density. Find the electric field at the symmetry plane of this sheet

Explanation

We can consider two sheets of thickness `(t/2-x)` and `(t/2+x)`
When a point lies inside the sheet.
Net electric field at point `P : E=E_(1)-E_(2)=Q_(1)/(2Aepsi_(0))-Q_(2)/(2Aepsi_(0))`
[`Q_(1)` : charge on left sheet, `Q_(2=` change of right sheet]
`=(AP (t/2+x)-2rhoA(t/2-x))/(2Aepsi_(0))=(rho[3x-t/2])/(2epsi_(0))`
At the symmetry plane, `x=0` So, `E=-(rho t)/(4 epsi_(0))`