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.
To find the electric field just above the middle of the sheet, we can use the equation for the electric field due to a flat sheet of charge, which is given by:
E = σ / (2ε₀)
Where:
E is the electric field
σ is the charge per unit area
ε₀ is the permittivity of free space
In this case, we are given that the charge per unit area is 2.05 µC/m². However, we need to convert this charge to Coulombs per square meter (C/m²) before using it in the equation.
To convert µC/m² to C/m², we can use the fact that 1 µC = 10^(-6) C. So, 2.05 µC/m² is equivalent to 2.05 × 10^(-6) C/m².
Now we can substitute the given charge per unit area into the equation:
E = (2.05 × 10^(-6) C/m²) / (2ε₀)
The permittivity of free space, ε₀, has a value of 8.85 × 10^(-12) C²/N·m².
Substituting the value of ε₀ into the equation:
E = (2.05 × 10^(-6) C/m²) / (2 × 8.85 × 10^(-12) C²/N·m²)
Now we can calculate the electric field just above the middle of the sheet.