How Is Surface Charge Density Calculated from Electric Field Magnitude?

[pat666]

Homework Statement

A large plane having uniform charge density has an electric field just outside the plane that points directly toward the plane with magnitude 1.50×10^4 N/C .

What is the surface charge density?
Express your answer with the appropriate unit

Homework Equations

I am not sure how to start this, the relevant equations would probably be enough to get me through this questions.

The Attempt at a Solution

 

[aim1732]

Right. By Gauss Law electric field of an infinitely large plane non-conducting sheet is σ/2ε where σ is charge density and ε is permittivity of free space.

 

[pat666]

thanks for that, what is the permittivity of free space? also is this meant to be an easy question?

 

[aim1732]

Permittivity constant accounts the dielectric properties of the medium and for air(or vacuum) it is 8.854×10⁻¹² Fm^-1.
Remember the constant in the Coulomb's Law? It is actually 1/4πε .
As for the question itself if you are familiar with Gauss law it shouldn't be difficult and the result is used as a standard formula in many texts.

 

[rwisz]

The surface charge density is a measure of the amount of electric charge per unit area on a surface. It is typically represented by the symbol σ and is expressed in units of coulombs per square meter (C/m^2).

To find the surface charge density in this scenario, we can use the equation:

σ = ε0 * E

Where σ is the surface charge density, ε0 is the permittivity of free space (8.85×10^-12 C^2/N*m^2), and E is the electric field strength (1.50×10^4 N/C).

Plugging in the given values, we get:

σ = (8.85×10^-12 C^2/N*m^2) * (1.50×10^4 N/C) = 1.33×10^-7 C/m^2

Therefore, the surface charge density is 1.33×10^-7 C/m^2.