A large plane having uniform charge density has an electric field just outside the plane that points directly toward the plane with magnitude 1.25×104N/C .
What is the surface charge density?
Express your answer with the appropriate units.
To find the surface charge density, we can use the relationship between electric field and charge density for a uniformly charged plane.
The electric field just outside the plane of charge is given as 1.25×10^4 N/C. This electric field is pointing directly toward the plane.
The relationship between electric field and charge density for a uniformly charged plane is given by:
E = σ / (2ε₀),
where E is the electric field, σ is the surface charge density, and ε₀ is the permittivity of free space.
From the given information, we know that the electric field (E) is 1.25 × 10^4 N/C.
Plugging these values into the equation, we can solve for the surface charge density (σ):
1.25 × 10^4 N/C = σ / (2ε₀).
We know the value of ε₀, which is approximately 8.85 × 10^(-12) C^2/(N⋅m^2).
Now, let's solve for σ:
σ = (2ε₀) × (1.25 × 10^4 N/C).
σ = 2 × 8.85 × 10^(-12) C^2/(N⋅m^2) × 1.25 × 10^4 N/C.
σ = 2.21 × 10^(-7) C/m².
Therefore, the surface charge density is 2.21 × 10^(-7) C/m².
To determine the surface charge density of a large plane with uniform charge density, we can use the formula that relates electric field (E) to the surface charge density (σ):
E = σ/2ε₀
where ε₀ is the permittivity of free space.
In this case, the magnitude of the electric field just outside the plane is given as 1.25×10^4 N/C. Therefore, we can write:
1.25×10^4 N/C = σ/2ε₀
To solve for σ, we need to know the value of ε₀. The value of ε₀ is a fundamental constant equal to 8.85×10^(-12) C^2/(N·m^2).
Substituting the value of ε₀ into the equation, we have:
1.25×10^4 N/C = σ / (2 × 8.85×10^(-12) C^2/(N·m^2))
Simplifying the equation, we can multiply both sides by 2ε₀:
1.25×10^4 N/C × 2 × 8.85×10^(-12) C^2/(N·m^2) = σ
Calculating the result:
σ = 2 × 1.25×10^4 N/C × 8.85×10^(-12) C^2/(N·m^2)
Therefore, the surface charge density is given by:
σ = 2.213 × 10^(-6) C/m^2
The surface charge density is 2.213 × 10^(-6) C/m^2.