Answer:
The required area of the plates should be approximately 1.77 square meters to create an electric field of 47500 N/C.
Step-by-step explanation:
To calculate the required area of the plates to create an electric field of 47500 N/C, we can use the formula for the electric field between two parallel plates:
Electric field (E) = Charge density (σ) / (ε₀ * εᵣ),
where:
E is the electric field strength (47500 N/C in this case).
σ is the charge density on the plates (7.58x10^-9 C).
ε₀ is the vacuum permittivity constant (approximately 8.85x10^-12 F/m).
εᵣ is the relative permittivity (also known as the dielectric constant) between the plates. We will assume that there is air between the plates, so εᵣ for air is approximately 1.
Now, let's rearrange the formula to solve for the area (A) of the plates:
Area (A) = σ / (ε₀ * εᵣ * E).
Plugging in the given values:
Area (A) = 7.58x10^-9 C / (8.85x10^-12 F/m * 1 * 47500 N/C).
Area (A) ≈ 1.77 m².
So, the required area of the plates should be approximately 1.77 square meters to create an electric field of 47500 N/C.