Faradays experiments showed:
Direct proportionaluty between electric flux and charge on the inner sphere. And fortunately for us the constant of proportionality depended on the units used. And thanks to our standard engineers friendly SI units we got that proportionality constant equal to 1. Giving us a simple uncomplicated equation:
Ψ = Q
Where obviously Ψ(psi) means Electric Flux and Q means the charge. Giving unit of electric flux as Coulomb.
Electric Flux density or electric flux per unit area measured in columbs/sqr metres denoted by D, is a vector field and is member of “flux density” class of vector fields as opposed to “force fields” class as like electric field intensity.
The general formula for electric flux density is:
As above equation is restricted to only vaccum, it is not restricted to soely to field of the point charge. For a general point charge distribution in free space the equation is:
Leading to flux density be equal to:
Lets end the topic with an example.
Example: Find D in the region about the line charge 8nC/m lying along the z axis in free space.
Answer: The electric Field E
At p = 3m and E = 47.9ap V/m.
The value at p = 3m is D = .424ap nC/m.
The total flux leaving a 5 m line charge is equal to the total charge on that length or Ψ = 40 nC. Ans.