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 find the electric flux density ( mathbf{D} ) due to a uniform surface charge density ( sigma ) located in the plane ( z = 2 ), we can use Gauss’s law.

The electric flux density ( mathbf{D} ) near an infinite plane sheet of charge is given by:

[

mathbf{D} = frac{sigma}{2} hat{n}

]

where ( hat{n} ) is the unit normal vector pointing away from the surface. The surface charge density ( sigma = 2 , mu C/m^2 = 2 times 10^{-6} , C/m^2 ).

The normal vector ( hat{n} ) points in the positive ( z )-direction since the sheet is placed at ( z = 2 ) and we are considering points above the sheet.

Calculating the flux density ( mathbf{D} ):

[

mathbf{D} = frac{2 times 10^{-6} , C/m^2}{2} hat{k} = 10^{-6} , C/m^2 hat{k}

]

Since the point ( P(1, 1, 1) ) is below the plane at ( z = 2 ), we should consider the contribution of the plane charge in the ( z = 1 ) direction (down