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Physical and vector fluxes

The Maxwell’s law for the electric flux ΦD of the vector of the electric induction
D says that ΦD through any closed surface s is equal to the exciting the electric
field charge q that is located in the space region inside s. This could be
expressed mathematically:

(12)               ΦD=q

(13)                  <∫∫> D ∙ ds = q

(s)

If the normal +n of the surface s and the vector D form angle β then the flux
Φ D could be defined as:

(14)

(15)


Φd = ∫∫ D ∙ ds = D ∙ s = D.s cos β

(s)

dΦd = D ∙ ds = D ∙ ds cos β

Fig. 4 The flux ΦDof the vector of the electric induction D through surface s. If
the surface s is closed then Φd = q. Modified from Zlatev (1972)


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