Ahuge (essentially infinite) horizontal nonconducting sheet 10.0 cm thick has charge uniformly spread over both faces. the upper face carries +95.0 nc/m2 while the lower face carries -25.0 nc/ m2. what is the magnitude of the electric field at a point within the sheet 2.00 cm below the upper face? (ε0 = 8.85 × 10-12 c2/n · m2)
7.91 * 10^3 N/C
Explanation: In order to solve this problem we have to use the Gaussian law, in both charged surface for the infinite plane.
So inside the non conducting sheet we apply teh superposition principle adding the electric field from each charged surface.
Then we have
Adding the electric fields we have:
E inside= Eupper-Ebottom=(1/εo)*(σ+-σ-)= (1/8.85* 10^-12)*70 nC/m^2= 7.91* 10^3N/C
6.78 X 10³ N/C
Electric field near a charged infinite plate
= surface charge density / 2ε₀
Field will be perpendicular to the surface of the plate for both the charge density and direction of field will be same so they will add up.
Field due to charge density of +95.0 nC/m2
E₁ = 95 x 10⁻⁹ / 2 ε₀
Field due to charge density of -25.0 nC/m2
E₂ = 25 x 10⁻⁹ / 2ε₀
E = E₁ + E₂
= 95 x 10⁻⁹ / 2 ε₀ + 25 x 10⁻⁹ / 2ε₀
= 6.78 X 10³ N/C
THE GIVEN sheet can be taken as two horizontal force with surface charge density is
at one surface is ∈_1 =
at oher surface is ∈_2=
the magnitude of electric field due to surface charge is given as
So, electric field at P (2 CM below from surface is) = E_1 +E_2