Four infinitely large planar charged sheets are placed parallel to...

The electric field due to an infinitely large planar charged sheet is given by $E = \dfrac{\sigma}{2\epsilon_0}$, and it is independent of the distance from the sheet.

Let the rightward direction be positive.

Point P is located to the right of sheets 1, 2, and 3, and to the left of sheet 4.

Electric field at P due to sheet 1: $E_1 = \dfrac{3\sigma}{2\epsilon_0}$ (towards right)

Electric field at P due to sheet 2: $E_2 = \dfrac{\sigma}{2\epsilon_0}$ (towards right)

Electric field at P due to sheet 3: $E_3 = -\dfrac{2\sigma}{2\epsilon_0}$ (towards left, as it is negatively charged)

Electric field at P due to sheet 4: $E_4 = -\dfrac{4\sigma}{2\epsilon_0}$ (towards left, as it is positively charged and P is to its left)

Net electric field at P is the vector sum of these fields:

$E_{net} = E_1 + E_2 + E_3 + E_4$

$E_{net} = \dfrac{3\sigma}{2\epsilon_0} + \dfrac{\sigma}{2\epsilon_0} - \dfrac{2\sigma}{2\epsilon_0} - \dfrac{4\sigma}{2\epsilon_0}$

$E_{net} = \dfrac{3\sigma + \sigma - 2\sigma - 4\sigma}{2\epsilon_0} = \dfrac{-2\sigma}{2\epsilon_0} = -\dfrac{\sigma}{\epsilon_0}$

The magnitude of the electric field at point P is $\dfrac{\sigma}{\epsilon_0}$.

Answer: $\dfrac{\sigma}{\epsilon_0}$