The name is absent

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

Φ E = q-

ε

<∫∫ E ∙ ds = q

ε

(s)

where Φ_E 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 Φ_D could be
concentrated only in small region ∆s of the closed surface s, so we could
approximate:

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

(19)               ∆Φ_d = ∫∫ 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.

∆qdq
i = lim —=- = —-
∆t→0 ∆tdt

i = ∫∫ J ∙ ^ds =^φ J

(s)

—»

where J is the density ofthe electric current.

21

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