On a clear, sunny day, a vertical electrical field of about 118 N/C points down over flat ground. What is the surface charge density on the ground for these conditions?
To find the surface charge density on the ground, we need to use the equation:
σ = ε0 * E
Where:
σ is the surface charge density
ε0 is the permittivity of free space (approximately 8.85 x 10^-12 C^2/Nm^2)
E is the electric field strength
Given:
E = 118 N/C
By substituting the given values into the equation, we can calculate the surface charge density:
σ = (8.85 x 10^-12 C^2/Nm^2) * (118 N/C)
Calculating this gives:
σ ≈ 1.044 x 10^-9 C/m^2
Therefore, the surface charge density on the ground for these conditions is approximately 1.044 x 10^-9 C/m^2.
To find the surface charge density on the ground, we need to know the relationship between the electric field and the surface charge density. In this case, the electric field is given as 118 N/C pointing down, which means it is directed towards the ground.
The relationship between the electric field (E) and the surface charge density (σ) is given by Gauss's law:
E = σ / ε₀
Here, ε₀ (epsilon naught) is the permittivity of free space, which has a constant value of 8.854 x 10^(-12) C²/(N⋅m²).
Rearranging the formula, we find:
σ = E * ε₀
Substituting the given value for the electric field:
σ = 118 N/C * 8.854 x 10^(-12) C²/(N⋅m²)
Now, we can calculate the surface charge density:
σ ≈ 1.045 x 10^(-9) C/m²
So, the surface charge density on the ground under the given conditions is approximately 1.045 x 10^(-9) C/m².
Assume the ground is a conductor an use Gauss' law.
http://hyperphysics.phy-astr.gsu.edu/hbase/electric/gaulaw.html