1. Electrostatic field. Coulomb’s law. Gauss law (Электростатическое поле. Закон Кулона. Закон Гаусса)
Variables and units
Variable symbol Units
Charge q, Q Coulomb [C]
Linear charge density τ Coulomb/meter [C/m] (coulomb per meter)
Surface charge density σ Coulomb/meter2 [C/m2] (coulomb per squared meter)
Volume charge density ρ Coulomb / meter3 [C/m3] (coulomb per cubed meter)
Electric moment p Coulomb · meter [C·m]
(Электрический дипольный момент)
Displacement D Coulomb / meter2 [C/m2 ]
(Электрическое смещение)
Potential, Voltage U Volts [V]
Electric field strength/ E Volt / m [V/m]
Electric field intensity
Capacity C Farad [F]
Electric permittivity ɛ Farad / m [F/m]
Поле всегда описывается двумя характеристиками – напряжённость электрического поля и вектор электрического смещения.
An electrostatic field is a field created by electric charges that are stationary in space and unchangeable in time. An electric field is a special kind of matter associated with electric charges and transmitting the effects of charges on each other.
Coulomb’s Law. (ЗаконКулона)
Coulomb’s law consists of two statements:
1) The force between two charges q1 and q2 is proportional to both q1 and q2and also inversely proportional to the square of the distance between them:
2) The axis of the force lies on the direct line between the charges; it is repelling for like charges, and attractive for opposite charges.
The last equation is the third Newton's law: action is equal to antiaction.
Electric Field Strength e and Displacement Field d. (Напряжённостьисмещениеэлектрическогополя)
The electric field strength (intensity) is described by a vector quantity represented by the symbol E. It is defined as the force in the field per unit charge.
unit
– V/m
Force over the charge (читается так)
Field induced by the point charge placed somewhere:
defines a position of the point charge.
Displacement vector is also called electric
flux density:
Читаетсякак D equals to epsilon times E.
Gauss’ Law. (ЗаконГаусса)
Definition of the electric flux:
Total electric flux passing any closed surface is equal to the total charge enclosed by that surface.
Integral form:
Gauss law for the field displacement Gauss law for the field intensity
По-русски это постулат Максвелла А это закон Гаусса (приусловии постоянстваэпсилон, мы выносим его)
Differential
form
2. Poisson’s and Laplace’s equations for the potential of electric field (Уравнения Пуассона и Лапласа для потенциала электрического поля) Electric Potential. (Электрический потенциал)
It is a scalar value which may be used to describe properties of electrostatic field. And we may use only electric potential to describe electric filed.
A
n
electrostatic field may be described by different, but equivalent
terms:
1)
It is irrotational (безвихревой),
curl
.
It takes place if the field doesn't depend on time. (a)
And usually, it is assumed that there no electric current. (b)
It's not exactly true because even the current exists,
very often the potential may be introduced and
nevertheless, may be curl(E)=0, but sometimes not.
That is why there are general assumption of existing of electric potential (a and b)
2)
the integral
vanishes
3)
The integral
solely (только) depends on the
points A and B but not on the particular path taken from A to B.
Definition
of the potential:
