A uniform surface charge of σ = 2 μC/m2 , is situated at z = 2 plane. What is the value of flux density at P(1,1,1)m?

To determine the electric flux density (mathbf{D}) at point (P(1,1,1)) due to a uniform surface charge density (sigma = 2 , mu C/m^2) located at the plane (z = 2), we can refer to Gauss’s law in differential form:

[

nabla cdot mathbf{D} = rho_v

]

However, to apply Gauss’s law directly in this context, it’s easier to consider its integral form, especially since we are dealing with a surface charge in a specific location:

[

oint_S mathbf{D} cdot dmathbf{A} = Q_{enc}

]

Where (oint_S mathbf{D} cdot dmathbf{A}) is the electric flux through a closed surface (S) and (Q_{enc}) is the total charge enclosed by that surface. Since the point of interest (P) is not enclosed by the charged surface and the charge distribution lies entirely in a plane at (z=2), the scenario simplifies the analysis.

For an infinite plane with surface charge density (sigma), the electric field (E) (and thus, the flux density (mathbf{D})) is constant and perpendicular to the surface. By symmetry, above and below the plane, the electric field points away or towards the plane for positive