The name is absent



From the Maxwell’s law we could easily derive the Gauss’ theorem:

(16)


(17)


Φ E = q-

ε

<∫∫ E ds = q

ε

(s)

where ΦE is the flux of the vector of the electric intensity E through the closed
surface s. It is important to note that the full electric flux
ΦD could be
concentrated only in small region
s of the closed surface s, so we could
approximate:

(18)


Φ D = ∫∫ Dds = q

(∆s)


In other cases when the electric field is not concentrated in such small region but
we are interested to know the partial electric flux
∆ΦD through partial surface s
for which is responsible electric charge q it is appropriate to use the formula:

(19)               ∆Φd = ∫∫ D ds = ∆q

(s)

Electric current

The electric current i that is the flux of (positive) physical charges could be
defined using both scalar and vector quantities.

(20)

(21)


qdq
i = lim —=- = —-
t0 tdt

i = ∫∫ Jds =φ J

(s)

—»

where J is the density ofthe electric current.

21



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