Two infinite non-conducting plastic sheets, each10.0 cm thick

carry uniform charge densities σ1, σ2, σ3, and σ4 on their surfaces,

as shown in Figure 1. These surfaces charge densities have

the values σ1 = − 6 nCm−2

, σ2 = + 5 nCm−2

,

σ3 = + 2 nCm−2

and σ4 = + 4 nCm−2

Use Gauss’ law to find the magnitude and direction of the electric field at point A, in the

middle of the left – hand sheet

961 N/C to the left

Explanation:

The magnitude of the electric field due to an infinite non-conducting sheet is:

E = σ / (2ε₀),

where σ is the surface charge density (C/m²),

and ε₀ is the free space permittivity (8.85×10⁻¹² C²/(Nm²)).

The direction of the field is away from positive charges and towards negative charges.

σ₁ has a negative charge, so the electric field due to σ₁ will be to the left (-x direction).

σ₂, σ₃, and σ₄ have positive charges, so the electric field due to those surfaces will be to the left (-x direction).

The total electric field at A is therefore:

E = 1 / (2 × 8.85×10⁻¹² C²/(Nm²)) (-6×10⁻⁹ C/m² − 5×10⁻⁹ C/m² − 2×10⁻⁹ C/m² − 4×10⁻⁹ C/m²)

E = 5.65×10¹⁰ Nm²/C² (-5×10⁻⁹ C/m²)

E = -961 N/C