tài liệu cơ sở ngành văn cường ct

 Michael Faraday (1791-1867): Discovered that a time changing magnetic field.. produced an electric field, thus demonstrating that the fields were not independent.[r]

Luong Vinh Quoc Danh 1

Bài giảng: TRƯỜNG ĐIỆN TỪ (CT361)

(ELECTROMAGNETICS)

Chapter 4: Electrostatics

(Tĩnh điện học)

Giảng viên: GVC.TS Lương Vinh Quốc Danh Bộ môn Điện tử Viễn thơng, Khoa Cơng Nghệ

• Maxwell’s Equations

• Charge and Current Distributions • Coulomb’s Law

• Gauss’s Law

• Electric Scalar Potential

• Electrical Properties of Materials • Electric Boundary Conditions

Maxwell’s Equations

3

Modern Electromagnetism is based on a set of FOUR fundamental relations known as Maxwell’s Equations:

Where D = E ; B = H ; J = E

Historical Notes

 Charles A de Coulomb (1736-1806): Measured electric and magnetic forces

 André M Ampere (1775-1836): Produced a magnetic field using current – solenoid  Karl Friedrich Gauss (1777-1855): Discovered the Divergence theorem – Gauss’ theorem – and the basic laws of electrostatics

 Alessandro Volta (1745-1827): Invented the Voltaic cell

 Hans C Oersted (1777-1851): Discovered that electricity could produce magnetism  Michael Faraday (1791-1867): Discovered that a time changing magnetic field

produced an electric field, thus demonstrating that the fields were not independent  James Clerk Maxwell (1831-1879): Founded modern electromagnetic theory and predicted electromagnetic wave propagation

 Heinrich Rudolph Hertz (1857-1894): Confirmed Maxwell’s postulate of

Static Fields

5

Static fields: This happens when all charges are permanently fixed in space, or

move at a steady rate so that v and J are constant in time

Maxwell’s Equations reduce to: ( )

Charge and Current Distributions

Charge Densities:

 Volume charge density v:

 Surface charge density s:

Where q is the charge contained in v

Where q is the charge present across an elemental surface area s

Example 4-2: Surface charge distribution

7

Surface charge density s increases linearly with r

from zero at the center to C/m2 at r = cm Find

the total charge present on the disk surface

Solution:

Since s is symmetrical with respect to the angle ,

Current Density:

The amount of charge q flowing through s is:

The corresponding current is:

Review

• Convection current: current is generated by the actual

movement of electrically charged matter Convection current

occurs in dielectrics such as liquid, vacuum Convection current does not satisfy Ohm’s law.

Example: Wind-driven charge cloud, electron beams in a CRT.

 In a perfect dielectric,  =  J = E = 0

9

• Conduction current: Conduction current occurs in

conductors Conduction current occurs due to the drift motion

of electrons Conduction current obeys Ohm’s law.





J E

Conductivity:

(A/m2)

Current density:

(S/m)

(4.67) (4.66)

Source: http://www.qrg.northwestern.edu/projects/vss/docs/power/2-whats-electron-flow.html

Review

How fast electrons move in wires?

11

Faraday Cage

Cell phone and AM/FM radio in the open cage

and in the closed cage

Experiment: A Faraday cage blocks long wavelength EM waves but does not block

short wavelength EM waves.

Principle: Shielding of electromagnetic waves by a screen enclosure depends on the

wavelength of the EM waves and the size of the holes

Coulomb’s Law

(4.13)

Electric field intensity E:

Electric force acting on a test charge q’ is given by:

Electric flux intensity D:

With

Electric Field due to Multiple Point Charges

(4.19)

Example 4-3

Four point charges on the corners of a square, with Q1 = Q3 = 1C, and Q2 = Q4 = -1C

Demo

Electric field due to charge distributions

Example 4-4: Electric field of a ring of charge

19

Gauss’s Law (cont.)

(4.26)

Electric Scalar Potential

21

Work (công) needed to move a charge q:

l E d

q

dW   

 Differential electric potential (or differential voltage):

l E d

q dW

dV    

Fext: external force needed to

move the charge along the positive y-direction.

Fext = - Fe = - qE

(4.36)

Relating E to V

Flow inward The origin is a sink

Electric Potential Due to Charges

In electric circuits, we usually select a convenient node that we call ground and assign it zero reference voltage In free space and material media, we choose infinity as reference with V = Hence, at a point P

25     N i i i q V 4 1 R R  Multiple Charges: Charges distributions:

Electric Potential Due to Charges (cont.)

Example 4-7 (cont.)

Poisson’s Equation  v E       v

V  

 



 v

V  

2

V

E  

Laplacian

 V

Electrical Properties of Materials

 No free electrons

P = electric flux density induced by E

Polarization Field

Độ cảm điện

Boundary Conditions

Tangential Component Normal Component

Summary of Boundary Conditions

Conductors

When a conducting slab is placed in an external electric field E0, charges that accumulate on the conductor surfaces induce an internal electric field Ei = - E0 

The total field inside a conductor is zero.

35

The electric field lines point directly away from the conductor surface when s is

positive and directly toward the conductor surface when s is negative

Conductors

Fig 4.21

When a metallic sphere is placed in an electrostatic field, negative charges will accumulate on the lower hemisphere and positive charges will accumulate on the upper hemisphere.