Lecture (6 )
Electric Flux Density , Gauss’s law and Applications
2.4 Electric Flux Density ( Φ )
From the concept of electric field flux – to the calculation of electric fields of complex charge
distributions.
Applies to any vector field ⃗ = ( ⃗), the flux of the field ⃗ = ( ⃗) through a small element of
surface ⃗ is
For calculate the flux of uniform electric field through the surface shown in the figure.
By use the equation :
Therefor the value of flux is
Flux through closed surfaces , the net flux of the electric field is:
The integral is taken over the whole surface
We integrate over
this “Gaussian”
surface
Also any point charge at the center of a spherical surface the ⃗ ⃦
figure
⃗ ( Cos φ = 1 ) see the down
In this case the value of flux is
The flux doesn’t depend
on ( r )
The flux for point charge place outside the surface is equal to zero
The flux magnitudes for two surface same as in the down figure is taken same value.
Two surface
2.5 Gauss’s law – Maxwell’s Equation
2.6 Applications of Gauss’s law
For two parallel plates ( Conducting plates )
=
E=0
⃗
E=0
=
=
2σ1