Two flat metal plates of area 2.8 m2 are placed parallel to each other and both are then charged, one with +10 µC and the other with -10 µC. Determine the electric field in the air gap anywhere far from the edges.
To determine the electric field in the air gap between the charged metal plates, we will use the concept of the electric field due to charged parallel plates.
The electric field between parallel plates is given by the formula:
E = σ / ε₀
where E is the electric field, σ is the surface charge density, and ε₀ is the permittivity of free space.
First, let's calculate the surface charge density on the plates. The surface charge density is defined as the charge per unit area. We have two plates with charges of +10 µC and -10 µC, and an area of 2.8 m² each. Therefore, the surface charge density on each plate can be calculated as follows:
σ = Q / A
where σ is the surface charge density, Q is the charge on the plate, and A is the area of the plate.
For the positively charged plate:
σ₁ = (+10 µC) / (2.8 m²)
For the negatively charged plate:
σ₂ = (-10 µC) / (2.8 m²)
Now, using the formula for the electric field E = σ / ε₀, we can calculate the electric field in the air gap:
E = (σ₁ - σ₂) / ε₀
Substitute the values of σ₁, σ₂, and the value of ε₀ (which is approximately equal to 8.854 x 10⁻¹² C²/Nm²) into the equation to find the electric field E.
Remember to take care of the units during calculations, making sure that all the charges are in the same unit (Coulombs), and all the areas are in the same unit (square meters).
Once you plug in the values and perform the necessary calculations, you will be able to determine the electric field in the air gap between the parallel plates.