The figure shows portions of two large, parallel, non-conducting sheets, each with a fixed uniform charge on one side. The magnitudes of the surface charge densities are σ(+) = 4 μC/m2 for the positively charged sheet and σ(-) = 10 μC/m2 for the negatively charged sheet.
What is the magnitude of the electric field between the plates?
To find the magnitude of the electric field between the plates, you can use Gauss's Law or the concept of electric field due to a charged plane.
1. Using Gauss's Law:
a. Consider a Gaussian surface in the form of a rectangular box between the plates, with two sides parallel to the plates and two sides perpendicular to them.
b. Since the plates are parallel, the electric field is uniform between them.
c. The total electric flux passing through the Gaussian surface is given by Φ = E * A, where A is the area of the sides of the Gaussian surface parallel to the plates.
d. By Gauss's Law, Φ = Q_enclosed / ε₀, where Q_enclosed is the charge enclosed by the Gaussian surface and ε₀ is the vacuum permittivity (ε₀ ≈ 8.85 x 10^-12 C²/(N·m²)).
e. The charge enclosed by the Gaussian surface is the sum of the charges on the two plates: Q_enclosed = σ(+) * A + σ(-) * A = (σ(+) + σ(-)) * A.
f. Equating the two expressions for Φ, we have E * A = (σ(+) + σ(-)) * A / ε₀.
g. The area A cancels out, so the electric field E = (σ(+) + σ(-)) / ε₀.
2. Using the concept of electric field due to a charged plane:
a. The electric field due to a uniformly charged plane is given by E = σ / (2ε₀), where σ is the surface charge density and ε₀ is the vacuum permittivity.
b. For the positively charged sheet, σ(+) = 4 μC/m², so the electric field due to this sheet is E(+) = σ(+) / (2ε₀).
c. Similarly, for the negatively charged sheet, σ(-) = 10 μC/m², so the electric field due to this sheet is E(-) = σ(-) / (2ε₀).
d. Since the electric fields due to each sheet are in opposite directions, the net electric field between the plates is given by E = |E(+) - E(-)|.
Using either method, you can calculate the magnitude of the electric field between the plates by plugging in the values.