A large, flat, horizontal sheet of charge has a charge per unit area of 2.05 µC/m2. Find the electric field just above the middle of the sheet.
kN/C
To find the electric field just above the middle of the sheet, we can use the formula for the electric field due to a uniformly charged sheet. The formula is given as:
E = σ / (2ε₀)
Where:
E is the electric field
σ is the charge per unit area
ε₀ is the vacuum permittivity constant, which is approximately 8.85 x 10^-12 C^2/(N·m^2)
In this case, the charge per unit area (σ) is given as 2.05 µC/m², which can be converted to Coulombs per square meter by multiplying 2.05 µC by 10^-6:
σ = 2.05 µC/m² x 10^-6 C/µC = 2.05 x 10^-6 C/m²
Now, substituting the value of σ into the formula, we have:
E = (2.05 x 10^-6 C/m²) / (2ε₀)
Using the value of ε₀, which is 8.85 x 10^-12 C^2/(N·m^2), we can calculate the electric field:
E = (2.05 x 10^-6 C/m²) / (2 x 8.85 x 10^-12 C^2/(N·m^2))
Simplifying the expression, we get:
E ≈ 116.38 kN/C
Therefore, the electric field just above the middle of the sheet is approximately 116.38 kN/C.