Лекция 1_2022 презентация

Advanced chapters of
theoretical electroengineering.
HSHVPE, IE SPbPU, Prof. A.G. Kalimov 2022

General information
Общая информация
Лектор – Калимов Александр Гелиевич,
профессор ВШВЭ ИЭ СПбПУ
Базовая литература:
K. Binns, P. Lawrenson. Analysis and computation of electric
and magnetic field problems
К. Бинс, П. Лауренсон. Анализ и расчет электрических
и магнитных полей.
Дополнительная литература:
3. Gunther Lehner. Electromagnetic Field Theory for Engineers and
Physicists.

Analysis and computation of electromagnetic fields.

Fundamental concepts of electromagnetics.
Electrostatics.
Lecture 1
(after: Gunther Lehner. Electromagnetic Field Theory for Engineers and Physicists)

Vectors and scalar fields.

Operations with vectors. addition and subtraction
Components of the vector in the Cartesian coordinate system
Parallelogram and head-to-tail rules

Vector multiplication.
Dot product
If the vector components are known
Dot product or scalar product
The dot product of two same vectors is

Vector multiplication.
Cross product
Are the unit vectors in the Cartesian coordinate system
Cross product or vector product

Differential operations.
Gradient of a scalar field.
Designation:
In the Cartesian coordinate system:
Object of operation is a scalar field
Result of operation is a vector field

Divergence of a vector field.
Designation:
Result of operation is a scalar
In the Cartesian coordinate system:
Object of operation is a vector field

Circulation of a vector field.
In the Cartesian coordinate system:

Properties of the differential operators.
Differential operations are linear:
Important Vector Identities:

Differential operator Nabla.
In the vector algebra an operator is often used
In the Cartesian coordinate system:

Integral theorems.
Different forms of the Gauss theorem
Stoke’s theorem

Electrostatic field.

Variables and units
Variable symbol Units
Charge q, Q Coulomb [C]
Linear charge density τ Coulomb / meter [C/m]
Surface charge density σ Coulomb / meter2 [C/m2]
Volume charge density ρ Coulomb / meter3 [C/m3]
Electric moment p Coulomb · meter [C·m]
Displacement D Coulomb / meter2 [C/m2]
Potential , Voltage U Volts [V]
Electric field strength E Volt / m [V/m]
Capacity C Farad [F]
Electric permittivity ɛ Farad / m [F/m]

Coulomb’s Law
1. The force between two charges q1 and q2 is proportional to both q1 and q2 and 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.
Coulomb’s law consists of two statements:

Electric Field Strength E and Displacement Field D.
unit - V/m
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
Field induced by the point charge
Displacement vector is also called
electric flux density
unit - C/m2
defines a position of the point charge

Gauss’ Law.
Gauss law for
the field displacement
Total electric flux passing any closed surface is equal to the total charge enclosed by that surface
Gauss law for
the field intensity
Integral form:
Differential form:
The electric flux:

Electric Potential.
An electrostatic field may be described by different, but equivalent terms:
It is irrotational,
The integral vanishes
The integral solely depends
on the points A and B but not on the particular
path taken from A to B.

Work in the Electric Field.
The field performs work on charges
Conversely, to move the charge against the field requires one to do work.
The force,
The work
or
For infinitely remote point A: ;
The work against field forces: ; this work increases the field energy

Dielectric polarization.
Dielectric materials are polarized when an electric field is applied to them. As a
result, electric displacement becomes greater than under the free space condition:
The polarization is defined as the dipole moment per unit volume.
In isotropic and linear materials, the polarization is directly proportional to the electric field and the proportionality constant does not depend on the field

Dielectric material characteristics.
In the linear dielectric material the field intensity is proportional to the displacement
is the relative dielectric permittivity (dielectric constant)
is the dielectric permittivity (dielectric constant)
In the case of extremely high electric field the electrons will accelerate and collide with molecular lattice structure, which causes permanent damage to the material. This phenomenon is known as dielectric breakdown.

Properties of dielectric materials.