Answer:
E = 5.03 10⁻³ N / C
Explanation:
For this exercise we can use Gauss's law
Ф = E. dA = [tex]q_{int}[/tex] /ε₀
Where as a Gaussian surface we select a cylinder
Ф= E A = q_{int} /ε₀
Let's use the concept of surface charge density
σ = q / A
q = σ A
E A = σ A /ε₀
E = sig /ε₀
Since the plate is non-conductive, the fux does not flow through the plate
With this equation the electric field does not depend on the distance, so the field at 1 cm
E = 45 10³ N/C
σ = E ε₀
σ = 45 10³ 8.85 10⁻¹²
σ = 3.98 10⁻¹⁰ C / m²
As the point where the field is requested is very far from the plate we can not ignore the finite size of it
At r = 15 m the plate has a very small size, so let's calculate the field as created by a point load at this distance
E = k q / r²
The plate area is
A = L L
A = 0.75²
A = 0.5625 m²
q = σ A
q = 3.98 10⁻¹⁰ 0.5625
q = 1.26 10⁻¹⁰ C
Let's calculate
E = 8.99 10⁹ 1.26 10⁻¹⁰ / 15²
E = 5.03 10⁻³ N / C
